Sports betting is not legal in Texas and the prospects of that changing are bleak. Lawmakers introduced a sports betting bill in 2019, but it didn't go anywhere similar to other gambling expansion bills in the past. The governor has gone on record opposing any expansion of gambling and that even includes fantasy sports.
That said, residents can technically play Daily Fantasy Sports because they have yet to be addressed by legislation. While there have been numerous attempts to legalize fantasy sports since 2017, none of them have come to fruition. Some lawmakers in the state believe fantasy sports are considered illegal gambling, but there isn't anything official that prohibits people from playing DFS.
Of course, given how difficult it has been to get DFS legalized, it could be even tougher for sports betting. Horse racing betting is legal in Texas, but it can only be done in person.