Like brother Ibrahim Imran Atheism Refuted stated, the type of content that you have within your tournament definitely counts. If the tournament has anything that is haraam within it, then the prize money will be counted as haraam.
This fatwa states that if the competitions are not being funded by the people competing within them, then it is halaal.
You are charging a monthly fee to the players of these tournaments. If the tournament prize money comes from the monthly fee, then it is haraam. If the monthly fee is just for the right to enter the tournaments where a prize will be given then this fatwa states that it is still haraam. Read point 1 on that page as it states that paying a fee just so that there's a possibility of winning a prize is not permissible.
If there was no monthly fee then there would be zero loss on the player's side, but since there is a monthly fee there is something to be lost.
Think of it like playing the lottery. I pay up front for the right to enter the lottery (monthly fee). I choose numbers not knowing if they'll come out (enter tournament not knowing if I will win). If I win the lottery I make money (If I win the tournament I win money).