Fake. The 1985 VHS did not have the 1999 DVD audio for one thing (which is very obvious), and for another it did not have the trailer for The Naked Time on the end, but for The Corbomite Maneuver.
You're right, this does have the added DVD sound effects (the transporter and the bridge background sounds). Why would this guy bother with that?
The actual question, though, was whether the early video release had the blue Paramount logo at the end. I think they did. Paramount slapped them on every episode when they redid the prints for video release and syndication in the 80's. I clipped them when I made DVDs of the lasers, keeping on the Desilu logo.