Even though I tried to stop playing, I could not stop.
This is grammatically correct. It means that, at some time in the past, you did try to stop playing, but you were unable to stop at the time. It's all in the past, so either you stopped trying (and still play) or you have since found some way of stopping. If that's what you really meant to say, it's perfect.
If you intended to say that you are are still trying to stop, but you still haven't been successful, you would say:
Even though I have tried to stop playing, I can't stop.
The first uses the simple perfect (tried) which describes a completed action, and the second uses the present perfect simple (have tried) which describes something that started in the past and is ongoing.
The tense of the second verb (could/can) must change to match the tense of the first verb.