Yes and no. The objective of mahjong is to be the player with the most points after the final round. It is possible to play the game for money, in which case these points can correlate to money in some way. Mahjong is often played without money, though, in which case the points merely determine the winner.
Gambling, other than betting on horse races or the government-sponsored Thai lottery, is prohibited in Thailand. The prohibition dates back to the Gambling Act 1935. The Playing Cards Act prohibits private ownership of more than 120 playing cards without approval of the government.