"Edrychais i ar y teledu."
Translation:I watched the television.
There is also a difference between "gwylio" to watch and "edrych ar" to look at, so literally the sentence means "I looked at the television". For your example of keeping an eye on a TV you could say "gwyliais i'r teledu", which you would never use for "I watched television".
To sum up, "edrychais i ar y teledu" literally translates as "I looked at the television", but in practice it means "I watched television", the word "y" being there because that's how the language works, not because it is a particular television. Tell me if this isn't clear!