it is a nuisance and it changes from browser to browser. 
The short answer is to close all browser windows and tabs but the one you are playing the game into in order to decrease the amount of processes you have to check and start checking the process using more memory or most cpu time (task manager). Other workarounds are to play games on a different browser, like one of the forks that still use single process model.

If you are not afraid to be more techy then there is a way to know for sure which is the right process. The gist of it is that the correct process is the process of the tab you are playing the game into, with the extra annoyance that if the game is embedded in it then there will be a subframe process ( works like that in chrome) and that will be it not the whole tab process. 

Chrome has a task manager that tells you process data for a window if you are wondering how to get the pid for firefox i dont know if there are tools
Lastly if you try and dont find any result you can be sure you opened the wrong process