I think it's an issue of word order logic. Emphasis on the end of the sentence means that previously known bits of information find their way closer to the beginning of the sentence. Here, the definite article "the" means everyone taking part in the conversation would know which movies are being discussed.
My hunch is that "I do not have the movies" would be translated as «Фильмов у меня нет.»
I believe that one-syllable words like "стол" tend to have the grammatical suffix stressed...what confuses me is that the "о" in "фильмов" is pronounced like a proper "o" sound in this case even though it is not stressed, any explanations for this ? Or maybe the audio is just off here, since it is supposed to be pronounced like an "a" sound like it is in "студентов" for example...
The unstressed о sound isn't actually an /a/, it's an /ə/, also known as a schwa. Loosely, it's the sound halfway between o and a. Depending on a bunch of factors like the preceding consonant, the following consonant, even the speaker, it may sound closer to an o or closer to an a. Very hard consonants like мъ / въ / бъ tend to bring the lips outwards in an effort to separate the palate and the tongue, shifting the vowels surrounding them towards an /o/ sound.
Look for words that are heavy on those and pay attention to how different speakers pronounce them, I'm sure you'll notice it for yourself. A very clear example is пробовал: as you can see, it's much closer to "probovol" than it is to "probaval." :-)