So, it's not really a definition but more of an explanation and attempted proof.

As far as a definition, no definition should be required ... if it's true that BoD is some kind of dogma and its denial heretical.  Church does not and cannot demand the assent of faith to a word or phrase, but only to propositions.  We can't just believe in a "BoD" without knowing what it is that we must believe about it.  So the very fact that there are many "definitions" floating around is in fact prima facie evident that it's never been defined.

Now, as far as articulations or explanations of BoD go ... this one is actually fairly solid and is not heretical (like most of them).  He's very careful to avoid making the heretical statement that we can be saved without Baptism, but says we can be saved without ACTUAL (reception of) Baptism.  That's the language of St. Robert Bellarmine who was very carefuly to put it that way to avoid the impression of denying Trent's dogmatic teaching that Baptism is necessary for salvation, since if you claimed that one can be saved WITHOUT it, that would be heretical.  But most people today are sloppy and invariably define it heretically.

So this is acceptable as an explanation or articulation.

Now, the proofs he adduces are dishonest, taken out of context, misapplied, and just nonsensical.  I could take the time to refute them, but won't.  I don't believe that BoD exists, but if it did, this would be the proper way to explain and articulate it.

Yeah, I've never "condemned" anyone as a heretic JUST for believing in BoD, since it's clearly been tolerated and even at times favored by the Church, BoD meaning that one could be SAVED without the ACTUAL reception of the Sacrament of Baptism, i.e. by receiving Baptism in voto.  That's one of the points on which I disagree with the Dimond Brothers.  Now, I do believe that it's OBJECTIVELY heretical, but the Church hasn't defined otherwise.  I believe there are two dogmatic definitions which all but excluded a BoD in the sense of it being capable of bringing SALVATION, but it's still my interpretation of those.  What I mean by that, i.e. it being objectively heretical, is the equivalent of ... if I were to have held before Vatican II that papal infallibility is a dogma.  So, in once sense I would have been right, because dogmas were all revealed from the beginning, objectively speaking, but in another it hadn't been proposed with sufficient clarity by the Church's authority so that someone denying papal infallibility before Vatican I would be considered a heretic.

I'm not going to refute the "proofs" adduced in detail, just to say that St. Ambrose says that the state of unbaptized martyrs is that of having been "washed but now crowned" (and then hopes that Valentinian might experience something like that by his piety and zeal) ... and elsewhere he says explicilty that even the best catechumens who die without Baptism cannot enter the Kingdom.  St. Augustine later retracted his opinion.  And that's really it.

I wouldn't spend 5 minute arguing against someone (other than in a friendly or academic way) who held this particular definition of BoD.  Now, the next question is whether, given how it's defined, whether some Jew who rejects Christ can be saved by this BoD.  That's a secondary question, and many err gravely by advocating for an IMPLICIT BoD.  But, again ... I won't go there for now.

Let us have a scenario for those interested (unafraid of either BOD or "Feenyite" nuclear contamination).

Titus and Paul are fellow miners.
Titus is a baptized, practicing Catholic in good standing with the Church - he strives to learn his faith and live it well.
Paul is a pagan - he worships one of his ancestor's petrified thumbs - in a makeshift shrine that he has set up at his home.
One day at work, there is a sudden and unexpected cave-in at the mine.
Titus and Paul are trapped deep within the mine and will soon die from lack of air, water, and food (which sadly - they have none of).
Not a drop of water in the whole darn place - dry as a bone...
To make matters worse...
Titus is trapped under the rubble - his arms and body are pinned under hundreds of pounds of debris!
He won't last long....
Prior to this event, Titus and Paul had been discussing Catholicism for several months and Paul is actually quite interested. He has the basic catechism down.
He was planning on telling Titus today that he wanted to meet with the priest to become an official catechumen and he is going to destroy his idolatrous thumb when he gets home.
Now, here in this terrible situation seeing - Titus pinned down, dying, and the prospect of his own life to end soon thereafter...He wants to belong to Christ's Church.
He expresses this to Titus.

And you as Titus say;

A) Sorry buddy, you are screwed. There is no way for me to baptize you. We have no water, nor do I have the use of my arms. You should have decided before now.

B) God sees your desire to belong to His Church - it is He who has given it to thee. Let us be truly sorry for all our sins ( Titus assists Paul in an examination of conscience...) Let us make a Perfect Act of Contrition and follow with an Act of Spiritual Communion - if more time remains let us continue to invoke the assistance of the Blessed Virgin. Let us trust in the mercy of God and He shall not abandon us - lest it is for something we have done without being truly repentant He is perfectly just. We can take great peace in this truth - He is merciful as He is just. Of all your mighty works O Lord none is so great as Thy mercy.

C) The Guardian Angel of Titus heaves the debris aside - a spring of fresh water miraculously gushes forth from the ground - Titus baptizes Paul - then they both drown together due to the water filling up the cavern of the mine shaft from the miraculous spring of water... Oh yeah, and we have no doubt about the validity of Paul's baptism - full immersion baby!

Is A) a lie?
Is B) a lie?
Is C) the only doctrinally sound position?

Maybe you have another answer in mind...

Yeah, the answer is that you guys are faithless and act as if God doesn't exist.  How about if it was God's will for Paul to be baptized He wouldn't have allowed him to be trapped in a cave with absolutely not a drop of water available?  In the lives of the saints there are several incidents where God miraculously had a font of water spring up precisely to allow a last-minute Baptism.  Similarly, in this case, without even having to work a miracle, the ordinary action of God's Providence would have arranged it so these two clowns would have been stuck in a cave that had at least some water in it, but I guess He couldn't prevent them from wandering into perhaps the .5% of all caves that have no water in them.

Epic fail, where you demonstrate here precisely how BoDers are faithless and act as if God doesn't exist and is somehow constrained by "impossibility" and forced to provide alternative means for salvation due to various "impossible circuмstances" (even made up crap like this) since He's not capable of managing it.

If any of your attitudes get me indignant it's stuff like this, where you show a complete lack of faith in God's Providence and in God Himself.

But, just be honest with yourself, you make up hypothetical crap like this just to justify your belief in BoD, caring nothing for the fact that you do so at the expense of showing that you have almost no faith in God.

Come up with some other reasons for BoD other than these "impossible" scenarios.

I got a BoDer into a corner once by asking Him that if God's Providence arranges for everything, why then would He will for someone to be saved by BoD rather than by arranging for him to be Baptized, which He could easily do?

He had no answer once it was put to him like that.  In stead sir-spam-a-lot responded by pasting in a bunch of statements from various Catholics who believed in BoD.

As I mentioned, I'm not going to arrogate the Church's authority unto myself by condemning as heretics anyone who believes in BoD ... as it was explained in the post in the OP, provided you don't then also go on to layer "implicit" BoD onto it for Jews who blaspheme Christ and Prots who blaspheme Our Lady, and where your "Baptism of Desire" has absolutely no connection to Baptism, since an individual has never even heard of Baptism, etc. etc.  In other words, if you can articulate a position on BoD that doesn't entail Pelagianism, denial of the necessity of the Sacrament of Baptism for salvation, or a general lack of faith in God (justifying it by nonsense like the fake story above) ... then I will not say you're a heretic.

But maybe 1% of the BoDers I've ever run into do not fall into one heresy or another in articulating "BoD", and where it's clear that they don't actually believe that there's no salvation outside the Church, but merely pay it lip service and apply to it the "understanding of the Church", where evidently the Church has its own understanding and interpretation of he word "not" and "absolutely no" than most people do.

At the end of the day, the pro-BoD zealots almost never actually care about the rare case of a Catechumen dying in a car crash on the way to his scheduled Baptism, or the bizarre hypothetical situation above ... but they're devoted to BoD since it allows them to reject EENS dogma while pretending to accept it and paying lip service to it.  That's really what it's about ... gettting various Prots and other "good" people saved.