Does "gospel-preaching church" have a shared meaning? Does "gospel-preaching church" have a shared meaning among Christians? What is it supposed to mean, and what are the signs of this "gospel-preaching church"? Is the term a tautology? Or is the negation of the term a way to criticize and slight other types of Christians or denominations that one group of Christians may disapprove of or dislike? If possible, where did this phrase come from, and by whom is this phrase typically used?
The term is not one that has an official definition across the board.  However, there are two meanings that are generally implied by the phrase.  One is a bit.. inflammatory, even if it's not really "meant to be taken that way".  It is tied up with the idea (common to most Christians) that some Churches are preaching a false "gospel".  (I say it's common to most Christians because if it weren't, we wouldn't have so much division within the umbrella of what's called "Christianity".)  The other is less inflammatory.



Starting with the inflammatory meaning, to get it out of the way:

It's something usually said by mainstream evangelicals, and in typical usage, it means "A church that preaches what my Church preaches.

To clarify that, most denominations agree on the central tenets of Christianity, but there are disagreements on certain points.
 - Some denominations teach a works-based salvation, or faith+works salvation.
 - Others are perhaps unfairly accused of teaching a works+faith salvation message.
 - Some denominations preach a Gospel message at the end of every service, and may include an invitation, while others don't.  (I don't recall any such thing ever occurring in a Catholic or Lutheran service, come to think of it.  Just the fiercely evangelical denominations.)

But typically, when you hear this phrase, it's a standard Evangelical protestant, who is a strong believer in salvation by faith alone.  And they're saying, in effect, "Go ahead and go to a Baptist Church, or an Evangelical Free, or an Assembly of God, even, they all differ in some ways, but they all have the right message on what it takes to be saved.  But don't go to that Catholic Church, they teach that you're saved by obedience to the Church, ordinances, and believe all kinds of wacky stuff like praying to saints and Transubstantiation.  Steer clear of them and stick to the churches that teach the real Gospel message.  And don't even get me started on them Mormons or Jehovah's Witnesses.  Go find you a Church that teaches that you're a sinner, that you need to repent and put your faith in Jesus, and trust in that alone!  Don't go to some Church that teaches anything not found in the Bible". 

(Again, shorter version, "Go to a Church that teaches what I believe.")



It can also have a less "I'm right, those heathens are wrong" meaning.  It can also simply mean, a Church whose focus is evangelism.  

As noted above, I don't recall ever hearing a message about having to repent, put my faith in Christ, and get saved in a Catholic Church.  (They may preach that, but I've just missed it...)  By contrast, every Baptist service, wedding, funeral, or pot-luck I've ever attended has a message, or at least a prayer that does this.  Also, you don't see a lot of Catholics going door-to-door handing out tracts, inviting people out to Church.  I see that in Baptist and other strongly Evangelical Churches (As well as with LDS and Jehovah's Witnesses) all the time.  So in that context, "Gospel Preaching Church" can simply mean a Church whose focus is on sharing the Gospel.