It's not the same. The "any" part isn't really found in "Hast du Brüder?"
What you propose would be "Hast du irgendwelche Brüder?"
I mean even in English, "Do you have brothers?" and "Do you have any brothers?" (or "Have you got any brothers" for that matter) is not the same, even though it's subtle.
difficult to hear what he says & in the slow version he does not say hast, but uses his breath for the 's' sound