I never really bother with closing other apps before playing a mobile game. But then I don't play those massive games like racing ones, the biggest one I have is Clash of Clans which doesn't need much RAM
Same for me, I usually close apps which I no longer need since having unused apps open may shorten my battery life, and make my other apps run slower.
I also don't like having so many apps in my recent apps section in Android because it makes finding other apps running in the background harder if I have many apps open in the recent apps section.
The only app that I might keep running in the background is OneDrive, because I tend to upload photos to it and then delete them from my mobile devices.