I wonder whether one can actually say 'I play computer every once in a while' instead of 'I play computer games every once in a while'. I haven't come across the former phrase in any written context and I doubt whether it can be considered grammatically correct.
Is it gramatically correct? I'm not sure. A computer is not something that can be played. You can play on the computer, and you can play a computer game.
Is it acceptable to say? Absolutely! I say "playing computer" all the time. Actually, I probably say this more often than "playing computer games". Everybody will understand your meaning, and I doubt that anybody would think it sounds strange.
Now, StoneyB has a good point, if you say "playing the computer" (or even "a computer") it implies you are playing against a computer. This would sound a little bit strange unless someone is asking who you are playing against.
What are you doing?
"I'm playing computer." OR "I'm playing on the computer." OR "I'm playing computer games."
These all sound perfectly fine.
Who are you playing against?
"I'm playing the computer." OR "I'm playing against the computer."
Both of these also sound fine.
Either you play something or play with/against something.
The verb 'play' is taking a direct object in first case, which is your concern. Purely in the context of 'gaming', the direct object is some game in almost all the cases.
Play football/cricket/rugby/chess and so on - All are games.
Play computer -seems no standard English (at least to me).
Even if it is grammatical, it's ambiguous for sure.
However, you may ...
"... play with/against the computer".
We say "play [game/sport]" such as in:
play soccer/chess/go (the game's name makes it definite and hence no definite article is used)
And we say "play the [instrument]" such as in:
play the piano
And we say "play with [the tool / tools]" such as in:
play with the computer / play with computers
And we say "play against [the opponent / opponents]" such as in:
play against the computer
And we say "play the [role]" such as in:
play the fool/king/thief/computer (the last one includes pretending to be a computer)
Also, note that Standard English requires the use of the definite article in "the computer", and omitting it is ungrammatical. This is because "the computer" refers to a generic computer, not a specific one (which "a computer" would refer to), and all count nouns need a determiner such as the definite or indefinite article.