And your TL is:
"If you play so many games, your eyes will get bad even if you don't know."
The part that you mistranslated, interestingly, is not even the "ても" part ("even if"). Rather it was the unmentioned subject of the verb 「知らない」.
It is the speaker who 知らない, not the game-player she is talking to. (I am envisioning a female speaker because of the わよ-ending.)
This 知らない, though very often used, is hard to translate, too. It does not mean "I do not know.". It is more like "Don't say I didn't tell you!" or "I won't be responsible (for that)!"
"You just keep playing games; Don't say I didn't tell you (not to) if your eyes went bad!"