Q: “We watched the game on the TV” sounds non-standard, while “We listened to the game on the radio” sounds perfectly fine. Why does “the” seem wrong when applied to TV, but OK when applied to radio?
A: The use of the definite article in fixed expressions like those is arbitrary and idiomatic. For example, you can listen “to the radio” or “on the radio,” but you communicate “by radio” and work “in radio.”
As Rodney Huddleston and Geoffrey K. Pullum explain in The Cambridge Grammar of the English Language, “A number of fixed expressions require the definite article. In such cases, it is largely arbitrary that the definite article is required rather than a bare noun (and often both are possible).”
Huddleston and Pullum note the use of “the definite article in expressions concerned with devices and institutions for the transfer of information, even though it is the activity or action that is relevant rather than the device used on a particular occasion.”
They cite “listened to the radio” and “spoke to her on the telephone,” where the definite article is necessary, but note that “the article is optional” in “watch something on (the) television” and not used in “watch (some) television.”
Searches with the News on the Web corpus, which tracks newspapers and magazines on the Internet, indicate that “on television” (91,933 hits) is much more popular than “on the television” (9,635). Nevertheless, dictionaries consider both versions standard English.
The wording of Merriam-Webster’s entry for the usage, “on (the) television,” indicates that the article is optional.
M-W defines the expression as “broadcast by television” or “being shown by television or in a television program.”
The dictionary includes these examples: “What is on the television tonight?” and “There’s nothing (I want to watch) on television right now.”
The authors of A Comprehensive Grammar of the English Language, Randolph Quirk et al., say the definite article is used in expressions like “the news, the radio, the television, the paper(s), the press, etc., referring to aspects of mass communication.” But they add that “with television or TV, there is also the possibility that the article will be omitted.”
Quirk includes these among his examples: “Did you hear the ten o’clock news?” … “What’s on the radio this evening?” … “What’s on (the) TV this evening?”
As we said at the beginning, the use of “the” in such expressions is idiomatic and arbitrary. Like you, we find “on TV” more natural than “on the TV,” but both versions are standard.