I don't know if it would qualify as a harem. To me a harem is everyone sleeping in the same bed and being friends. This is more guy banging a lot of chicks.
That's polyamory, not harem. Harem is simply distilled down to one guy, many girls, vice versa, or the same-sex variations. Whoever the many are, they can befriend each other or compete for the one's affections freely, without changing it being a harem.