How much "thought to animation and choreography" does it take to rotoscope someone else's animation and slap your own character over the top of it? If this was a parody, it would have added some sort of comment through additional humor. If it was a tribute, they would have had the respect not to obliterate the great animation by Ken Muse and Ray Patterson by pasting their own poorly traced drawings over the top of it. To my eyes, this looks like the Family Guy crew took the hard work of these legendary artists and copped it for themselves without adding a single thing to it. They can get away with it, because the viewers probably have never heard of Gene Kelly, much less have seen the clip of him dancing with Jerry Mouse.
You can see the clip for yourself here. As Worth says, it is the original Anchors Aweigh clip, with Stewie simply placed over Jerry.
I'm of two minds about this, and neither of them have anything to do with my feelings about Family Guy (you may not realize this because I've been so reticent about saying it, but I don't like that show). In an age when fewer and fewer young people are being exposed to classic animation and classic movies -- mostly because they're no longer shown on regular broadcast TV and most kids aren't going to be watching Turner Classic Movies -- it's something of a public service for Family Guy to be introducing its predominantly under-30 audience to the classics of both animation and live-action.
On the other hand, Worth is right that by simply re-tracing the original animation, the Family Guy crew is basically ripping off the hard work of Muse and Patterson. Look at the blog posts about the sequence: several of them pay tribute to the beautiful animation, without a real understanding that the animation has nothing to do with anything the Family Guy people did.
I suspect the segment was well-intentioned. But the way they did it, it does seem awfully like taking credit for other people's work. Creating new animation and/or live-action would obviously have not looked as good, but at least it would have been their own work.