Would both the sentences be commonly used?
(a) The more I play a computer game, the more I am absorbed in it.
(b) The more I play a computer game, the more absorbed I am in it.
I like (b) better. When it comes to computer games I think of the word "addicted".
The more I play a computer game , the more addeicted to it I become.
Also , I might say ....The more I play a computer game, the more absorbed in it I become.