Is it just me, or does it sound like it's saying "εχ" instead of "εχει"? Is it normal in Greece to drop the "-ει" ending?
I'm listening to it (on web) and it sounds fully pronounced to me. Having said that, Greeks can and do drop -ει endings, or at least they sound like they do to my ears.
Take a common word like εντάξει; in my experience, many native speakers will pronounce it as 'εντάξ', but with the ξ being very slightly more stressed and longer than usual.
But I haven't yet heard the -ει dropped on verbs like έχει, and wouldn't have thought it would be very often, because that part of the verb is essential to its meaning, and, quite often, to the overall meaning of the sentence.
I'd be interested in hearing a native speaker's opinion though.
I'm in agreement. "Εχει" is there but with the accent on the first syllable the second one rather gets swallowed. As spdl79 says it is often lost completely but there is enough here to be really normal.