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.
Obviously, it's gambling since you risk money on something for the expectation to win those pot money.
You are basically competing against those other players in the room. "Winners take all" therefore you compete for it.
And also if theres any known and trusted website or casino that allows such games. I find them better than gambling and lucky games
I think none. Maybe you can instead form a mini-tournament against your friends or those who played that game.
For example, in the famous game, 8-ball Pool, you can compete with your friends there or even form your own tournament with stake money.