That even one or two Coz restaurants offer a "traditional Thanksgiving dinner" really says something about how dependent Coz is on visitors from the US. It would be hard enough finding that in Mexico City--an enormous place where pretty much anything can be found. But that you can find it in little Cozumel really says something. I can see why Coz is so popular with American retirees.
I'm not sure where you've lived overseas, but everywhere I've lived one would be able to find Thanksgiving dinner in a restaurant. For that matter, I can find Bastille Day or Día de la Independencía menus or celebrations even in little ol' rural New Hampshire. The world is a big place and people travel all over it. People like a taste of home when they're far from there on holidays.
Add to that the fact that many outside a culture appreciate some of that culture's traditions - my German girlfriend loved Independence Day and Thanksgiving meals at our house, for example. My Mexican friends tend to love pumpkin and apple pies in particular, but given how Mexican turkey is, that's sort of a natural for them as well.
Americans flock to Italian, Mexican, French, Indian, and other "ethnic" restaurants and Mexicans love American food. That McDonald's back by Sam's and the Burger King on 30 aren't selling burgers to cruise passengers, nor is Kozumel Fried Chicken selling their "KFC" to many tourists. I haven't quite figured out why so many local families like Hooters so much, but they sure do.
I think you have the connection backwards. Cozumel offers 4th of July celebrations (and Oktoberfest, and more), traditional American holiday meals, and such because there are so many foreign retirees on the island - thousands of them! It's not tourists going to the parks for the 4th, it's locals, some of whom are islanders by birth and others of whom are islanders by choice. They all love a good hot dog and fireworks.
If I were on the island on Thanksgiving without a kitchen, I'd likely book a table at Rock 'n Java. Lisa knows what's up when it comes to food.
There are other American restaurateurs on the island, but I don't know how many of them will be doing a Thanksgiving menu.