The current popular sign for video game is one in which you hold both "A"
hands in front of you and alternately move your thumbs up and down as if
pressing a button on a "controller pad." To me, the sign looks a lot
like the sign for "texting." You can differentiate the two by doing
the sign for "texting" with the hands closely together and using very small
alternating thumb movements. Do the sign for "video gaming" by using a
more intense facial expression and bigger thumb movements.
You can also clarify (if needed) by using a separate sign for
GAME, or even signing MOVIE GAME to clearly
establish the noun "a game" form versus the verb form "gaming."
The older version of "video game" (the sign I grew up with) was based on
what was called a "joy stick."
Show the use of a "joy stick."