I wish to know if these games such as FPS which you can put for example in a room of 10 players everyone puts 5 dollars and the winner takes the whole 50 dollars, Are considered as gambling.
Provided money has been bet it's gambling. What you're doing here is relying on luck which can be associated with gambling. Most play to earn gamble comes with a contest that involves many players trying to win a prize by placing small bets and that's how they usually generate income to fund that completion.
For example when you organized a contest that involves the participants placing a bet of $5 and we have 100 participants that's $500 cash prize for one user to take all or shared between top winners, that's just the participants gambling. Gambling can be done in different forms and any activity can be gambled on