There's nothing distinct about the acting on TOS that's any different than what else, particularly dramas, was being aired at the time. I have shows on DVD from that era and there's nothing to set it apart.
Nothing but magnificence!
I've just been watching some early Mission: Impossible
and original The Outer Limits
and the acting style and so many other little details of television filming are very much like TOS. And on both shows you see so many TOS alumni.
Some interesting DNA trivia, too. Robert Justman worked on The Outer Limits
before Star Trek
so it's not surprising there's a lot of similarity in how stories were told. And Mission: Impossible
was also being produced at Desilu Studios so it's note surprising that there could be similarities in how the two shows were filmed and produced.