Sounds about normal for an AIO.  Yes, games can be played on it.  However, there's only 1 or 2 small fans cooling the whole thing.  There is also more heat buildup when monitor and PC are combined as one.  Small fans have to work at higher RPM's to move the same amount of air larger fans can do at a lower RPM.
Optiplex 7780 AIO  (Windows 10) When I play video games a fan comes on, sometimes quite loud.  Is this fan on the video card or is this fan for the CPU?  Or something else? It comes on when I play Halo and also with other games. Is this something to worry about?      
Fan comes on when I play video games