From the Texas Parks and Wildlife Outdoor Annual:

"Longbows, compound bows, or recurved bows:
- must have a 40 pound minimum draw at the time of hunting, when used to hunt turkey and all game anumals other than squirrel.
- that are equipped with a device that allows the bow to be locked at full or partial draw are lawful during any season when lawful archery equipment may be used.

Crossbow
Any person may use a crossbow to hunt game animals or game birds (except migratory game birds) during a general open season or Eastern spring turkey season. Telescopic sights are lawful.
ONLY a person with an upper-limb disability may use a crossbow to hunt deer and turkey during the Archery Only Open Season, provided the person, while hunting, has in their immediate possession a physician's statement certifiying the extent of the disability."

Seems like anyone wanting to hunt with a crossbow, at least in Texas, is free to do so. By the way, archery season here runs roughly from the first of October to the end of October while the general season, which is open to crossbow hunters, is from roughly the first of November to the first of January with a lot of counties having about a 2 week extended season for does and spikes. Seems plenty sensible and fair. By the way, those 2 fine young hunters could have taken those deer just as easily with a rifle as they did with a crossbow but they couldn't with a recurve OR crossbow.