Your own source says it.  pg2
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"The great mass of christians separated from the Catholic Church (i.e. protestants, heretics, schismatics...the Orthodox possibly being an exception because they "could" have valid priests) do not admit the teaching of the Church as to the sacramental character of marriage."
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Of course they don't.  They have no priests to give them a sacramental marriage, nor do they desire one, because to accept that marriage is a sacrament (as the article continues) they would "have to admit...that the Church alone...has jurisdiction over the marriage contract."

I think the Protestants would challenge that, and I know the Orthodox would.  When my cousin was married by a fundamentalist Protestant minister many years ago, I distinctly remember the minister referring to it as a "sacrament", and one reason I remember this, is that he pronounced it "SAY-kra-ment", which I found amusing.

Now whether ministers such as these understand "sacraments" in the same way we do, I do not know.  A better question might be "do you intend to confect this marriage as a sacrament in the way that the Catholic Church understands a 'sacrament', even though you reject the Roman Church's authority over the marriage contract".  I think the odd Anglican or Lutheran, at the very least, would say "yes".  Methodists and Presbyterians probably would too.
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There are 3 different classes/questions raised here.
1)  Could an orthodox couple have a sacramental marriage, being that they don't recognize the Roman Church as being their spiritual authority?  I'd say "no".

This would certainly come as news to them.

Their response would be more like "we do indeed have the sacraments, it's you who don't have them, because we are the One True Church, not you Latins".  I think it can be reasonably inferred that they intend to do what the Roman Church does.
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2) Could a protestant couple have a sacramental marriage, being they recognize no spiritual authority, except the Bible?  Obviously, no.

See above.
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3) Could a "mixed" couple (1 catholic, 1 baptized non-catholic) have a sacramental marriage?  I'm not sure, but logically I would say "no".  If the couple isn't united in their decision to follow the Church's authority (since one of the spouses is non-catholic), then how can the couple have a sacramental marriage?  The non-catholic spouse doesn't even believe that sacraments exist or are beneficial!  It makes no sense that a sacrament could exist, which is why the pre-V2 church made it a REQUIREMENT to get approval for a mixed-marriage...because the spiritual ramifications of having a non-sacramental marriage were so dangerous.
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If a marriage with a non-catholic, baptized spouse were a sacrament, then why was special permission needed at all?  I think this is self-explanatory.

I'd be interested to know what ++Lefebvre and ++Williamson would say about this.  Does anybody know?

They might say "yes, I intend a sacrament just the same as my catholic neighbors." but the reality is, if they don't believe in the Church's doctrines on 1) divorce/re-marriage, 2) contraception, 3) primary/secondary purposes of marriage, 4) raising of children, etc...then they don't have the basics for a sacramental marriage.  
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I've never heard of any protestant who agrees with the Church on all 4 of the above.  All protestants (and orthdox too) have lax rules on divorce/re-marriage and most all say contraception is ok.  No sacrament is possible for such heretical views.
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That's true, but Protestants don't believe marriage is a sacrament (if they believe in sacraments at all), so they can't bestow what they don't believe in.  (This presumes that both protestants were validly baptized).

These are requirements for a NATURAL marriage, for the natural law.  A sacramental marriage requires one to believe/know of Church Doctrine.

Agree.  They need to understand/believe, 100% correctly, all doctrine related to the Church's definition of marriage.  The 4 things I listed (+ maybe a few more).
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No, that's debatable.  If someone believes in divorce, then they are a heretic and are contrary to Church teaching.  That wouldn't be a sacramental marriage, imo.
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Believing that your personal marriage "will last" is not the same thing as believing, doctrinally, that the Christ/Church say marriages "have to" last, under penalty of grave sin, the violation of your marriage vows, and eternal damnation.
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Thinking that "I believe i've found the right one and our marriage will last" is a sentimental ideal.  Thinking that "I am marrying this person and I MUST be true to them, and MAKE it work, as I am vowing before God", is a doctrinal principle.  Catholics can have both thoughts, but the latter one is required.

It is certain, therefore, that marriage contracted between baptized persons is a sacrament, even the so-called mixed marriage between a Catholic and a non-Catholic, provided the non-Catholic has been validly baptized. It is equally certain that marriage between unbaptized persons is not a sacrament in the strict sense of the word.

It is certain, therefore, that marriage contracted between baptized persons is a sacrament, even the so-called mixed marriage between a Catholic and a non-Catholic, provided the non-Catholic has been validly baptized.

This is too subjective.  They need to believe the Divine command in Genesis:  "Til death due us part".  And they need to believe that this applies to ALL valid marriages, because this is church doctrine.  Believing that a truth only applies to you personally, is not believing in the truth at all.  That's called subjectivism - "It's true for me, but may not be true for you."  Nonsense!  God's truths apply to all men, at all times, for all time.  Like gravity and death.

Did you read the canon law article?  He lays it all out.

You're arguing that a non-catholic can have access to catholic sacraments.  This is totally wrong.  I don't know where you got this idea??

When canon law speaks of "valid" they are speaking of sacramental validity (not natural law validity), because canon law is dealing with catholic ceremonies.  But when speaking of natural law marriages and validity, canon law doesn't address this, because it is only dealing with catholic marriages.  You can't apply canon law to non-catholic ceremonies/marriages and expect it to make sense.  That's not its purpose.