No, you don’t need a PS4 NEO to play PSVR games.
I suppose there has been enough confusion regarding the upcoming PlayStation VR, and its status with respect to the confirmed, but as of yet unrevealed, PlayStation 4 NEO, that Sony Worldwide Studios head Shuhei Yoshida thought to clear the air up. Speaking at ACGHK 2016 in Hong Kong (via CoverBased), Yoshida confirmed that all PlayStation VR games will in fact be playable with the regular PlayStation 4 systems on sale on the market right now, and of which 43.5 million have been sold worldwide already.
“All the PSVR (and future) titles will be playable on (normal) PS4,” Yoshida confirmed, hopefully laying any doubts anyone might have had to rest once and for all.
Of course, that isn’t to say that PlayStation VR games won’t perform better on a PlayStation 4 NEO- hypothetically, they just might (and common wisdom holds that the existence of the NEO owes itself to the PlayStation VR in the first place). But it seems like Sony will ensure that regular PS4 owners are not left behind in the dust, at least.