It's almost same with the Turkish word for apple, "elma" (or its obsolete/dialectal form "alma")
This is not a coincidence; Hungarian borrowed the word from a Turkic language, according to Wiktionary.
The 'a' sound in Hungarian is similar to the 'a' sound in 'father'. The audio is correct. It's an 'a' not an 'o'.
When I listen to the pronunciation, I hear "alma", but it sounds somewhere between "alma" and "oyma". Is this merely my pecularity, or is it in fact pronounced slightly like oyma?