Both words start with an unstressed syllable, so о is pronounced similar to а.
To be more exact, unstressed а and о sound the same, closer to А and with no lip rounding :). Which sound you find it similar to depends on which variety of English you speak—it may be U in "sun" or O in "hot", or even A in "cat".
The male voice is based off a Moscow actor, so his accent is fairly standard.
«две двери» does not use plural—it is Genitive singular here. And it is the first time I hear about natives using the stress on the ending in thins form.
A more usual variation would be using «двери́» in Prepositional, which would match the Locative-2 of some other feminine nouns (e.g., в крови́, в тени́, на оси́, в пыли́, в грязи́)
Aaah, spelling it out with the "of" explanation totally helped me get it. Thanks.