We all know that 8-liners are illegal under normal circumstances but what about if the game room is run with a non-profit LLC or non-profit association. What is the law for this?

There is no gambling exception for a non-profit charitable organization. The only special privilege they have is the authority to operate a charitable raffle, under the provisions of Chapter 2002 of the Occupations Code. (Look there for the restrictions on how they can conduct a raffle.) Several gameroom operators have attempted to structure their 8-Liner games into some kind of charitable raffle, but I am not aware of any which have been successful in this ruse.