Have been a campground host at Davis Mountains SP. A really neat activity is the tour at the MacDonald Observatory. Most folks only go to the evening star party, but to me the real treat was the daytime tour where you get to go inside the enclosure of one of the big telescopes.
Fort Davis National Historic Park will take a day if you really explore the place and look into the history.
The biggest issue the 16 year old will have is that the only cell tower serving Fort Davis is on the other side of the mountain from the campground. There is limited WiFi at a couple sites in the campground, but not enough to satisfy a 16 year old. You or that child will likely be driving to the top of the mountain several times daily so they can check there social media.
Chama is one of my favorite places in the world, but I love trains, especially steam trains.