There are different types of licenses in Texas, one where food is at least 51% of sales "restaurant" and one with no food requirements "bar". I don't think the door charge and seat fees would count towards the 51% threshold but only a lawyer could prudently answer that.
Yes, TABC commonly runs sting operations where they send in an underage shill to buy booze underage. How things proceed afterwards is at the discretion of the agents to an extent. Abrupt closure isn't common for a first-time basic offense, though it could be. TABC can also act if the agent believes the business has engaged in "moral turpitude". That can include a great many things, including poker.
Maybe the Lodge has had previous problems with underage service. Maybe this is a poker related action against the liquor license (not ruling the poker is illegal but that it is too immoral to allow poker to be played in a bar.)
FWIW, I have applied for various liquor permits in Texas and have a passing familiarity with the rules and the lack thereof -=- DrStrange