I mean ALL U.S. citizens and visitors who believe in the Founder's original intent of an "American" Thanksgiving praising God for His blessings.
Look, I could be wrong, but I think there are very few people who don't give thanks to god (in some form) for the freedoms and bounty of the U.S. and their ability to enjoy those freedoms and bounty. That's true for recent immigrants as well as descendents of immigrants. And that's the flip side of the coin of pondering the genius of the legal machinery that makes that possible. So, ya know, it's a pretty good idea to take a day off and ponder both.
On the other hand, the Pilgrims were deeply religious people. They probably would have seen god's handiwork in everything -- but they couldn't have imagined what was to come, i.e. Declaration of Independece, Revolutionary War, Constitution, etc. etc.
So, you can probably skip everything beyond the Pilgrims in giving thanks and just focus on them or you can give thanks for America as it now is...that's probably a private choice.