Judit, you are correct in American English, but Brits say "through" or "out of".
It's probably an older form that has disappeared from the UK; language use seems to change pretty quickly.
Unless you are in the North of England, in which case, cat looks out window.
There's no indication in this sentence of whether the cat is looking in or out, though. :)
What is the difference between "átnéz az ablakon" and "néz az ablakon?" Doesn't the second one also mean "looks through the window?"
Only in an artistic text, song lyrics, etc.:
But in a normal setting, "át" translates to "through". So, for the same reason you wouldn't throw out "through"...
I would say some preverb or postposition is needed with the window. If not "át", then "ki" (out), "be" (in), or a postposition for the noun: "át", "keresztül", etc.
kinéz az ablakon
benéz az ablakon
átnéz az ablakon
néz az ablakon át
néz az ablakon keresztül
Or, it could be looking at (watching) a fly, on the window:
"Egy legyet néz az ablakon."
No, it doesn't. If néz has an object, you could say, though, that "néz vmit az ablakon át/keresztül."
I thought "néz" meant "watch". Shouldn't "the cat watches through the window" be accepted as well?
But doesn't watch need an object? "The cat watches me through the window." "The cat watches the dog through the window"...