Wow your example is a good one. Both are correct. We use the definite article e.g. 'the' when we are being specific and the indefinite article e.g. 'a' when we are talking in general. So in theory when we say we are watching the television this should be in reference to a specific T.V. The fact that in common speech, both of your phrases are interchangeable, exposes a difficulty in giving you a definite answer.

Hello. 'The' is an article, articles in the English language are: a-an-the,articles are put before words when the word is countable. In the case of 'the', it is used when we are talking about a specific thing. So from the two sentences you have written , the second one would be correct if it is referred to a particular television in their house, if you are just generally saying that they are watching television anywhere, then 'the' will not be used. You can also refer to this website for further information : https://dictionaryblog.cambridge.org/2015/08/19/a-an-and-the-how-to-use-articles-in-english/ Hope this helps. Have a great day:)