Why not kočka in this case?
Kočka is nominative. You need the accusative (kočku) here, as the direct object of the verb.
Why not "No, I see the cat"? With the stress on I see. Then the important thing is who sees the cat, not if it is a cat or something else.
That would be "Ne, já vidím tu kočku." But as Czech doesn't have a definite article it's a vague rule, it would be expressed like that here because it'd truly be about a specific cat.
Hey, is it sounds like "NE-vidim"or I have some problems with my hearing?
FWIW, on my system, it very clearly says "Ne, já vidím...." at both normal and slow speed.
That's looks little non-czech. Afaik when there is a negative word (like ne) everything should be in negative form
Not at all! This sentence is about contrast.
Alžběta asks Bartoloměj: Bartoloměji, vidíš psa?
Bartoloměj: Ne, (já) vidím kočku.