I have read this quote before and I have always thought that it sounds a bit self-centered, like if the priest was there simply to be a priest, and that the faithful are a nuisance that they have to deal with.

I suspect they keep the definition brief and limited so as not indicate that they are establishing a parallel diocese. The SSPX makes it a point to focus on the Priesthood and that is it, so as to send a message to the Vatican and local bishops that they are not trying to overstep their bounds/ jurisdictionction.  

Yet the definition is vague enough, that one can also imply the SSPX has a bigger mission (parishes, schools, retreats, book publishing business) than just preserving the Mass and Priesthood.

One of the problems of trying to normalize relations with Modernist while still trying to maintain your "customers", you have to be careful how you word statements as you need to satisfy two set of audiences with opposing views.

Example:

SSPX to Vatican: "Thank you for giving us jurisdictions for marriages, we will be sure to follow all your directives XOXO"
SSPX to SSPX Priest: "You better obtain jurisdiction before celebrating that marriage or else!" 
SSPX to laity: "Do not worry, our marriages have always been valid, if those nasty bishops do not give us jurisdiction, we will use supplied jurisdiction instead, so relax and have a drink"
Some guy in the back: "But did not Pope Francis said if a bishop does not give you jurisdiction that you can contact him directly and obtain jurisdiction, thus you have no need for supplied jurisdction? Also was this part of the strategy of gradualism that was planned at the GREC meetings?"
SSPX to the guy in the back: " Hush up you sedavacantist!"

https://sspx.org/en/eternal-priesthood-jesus-christ-30243

My underlining and boldening. I find nothing wrong here, but though "the salvation of souls" is implied in the words used, it helps to keep that fresh in the mind when the words "salvation of souls" are actually used. Isn't that one of the problems with the Vat II docuмents: too little mention of the salvation of souls? Why preserve the priesthood if not for the salvation of souls? More than just the sacraments are needed today to save souls. I see and hear about the priests often doing just the minimum. No doubt they have a busy life and personal limitations (they are human after all), but still. And it doesn't just take priests to save souls, but holy priests, better yet, holy priests skilled in the work of bringing the faithful to sainthood. We all know that not every doctor or mechanic or house builder is good at what they do, and some do just the minimum, whether out of ignorance or intentionally. I've heard Bishop Williamson being quoted, back when he was rector of the seminary, as saying something along the lines of "An excellent priest makes good faithful, a good priest makes faithful that are not bad, a mediocre priest makes bad faithful, and a bad priest makes faithful that are totally lost."

If we get the leaders we deserve, and the salvation from or oppression by our enemies as we deserve, then make sure the church has priests and faithful worthy of good things. You want this crisis to end? Most of us should know it's nowhere near enough to call ourselves Traditional Catholics and to be Weekend Trads when we don't live the traditional faith at home, school, and work. How many trads really know what it means to be a Catholic? How many priests are making sure people understand that? How many priests truly understand what it means to continue the work of Christ? The Apostles pretty much lost who they were and became our Lord Jesus Christ in their own way zealously continuing his work. Let us not forget to pray for our priests frequently no matter how holy they seem to be, that they may help us to be the saints God deserves. Even Jesus needed help carrying his cross/burden. How much do we help each other carry their cross?

Not to mention.....valid priests.