You may well be right - but I don't think it's just a 1967 thing, I think it's a Star Trek thing. There's a definite "Star Trek" acting style, a little more theatrical than most other television.
Have you watched any of Star Trek's contemporaries? In general its acting style was industry standard for the time.
Some, but not recently. (I remember seeing a lot of "Bewitched" and "I Love Lucy" as a kid, and a fair bit of "The Addams Family".) Admittedly, it was more common in those days for actors to have a theatrical background, meaning that everything had to be bigger so that people in the back row would be able to see. Nowadays, most actors are just TV or movie actors, and very few have done a lot of professional theatre.
I still think that there's a distinct Star Trek style of acting - if you watch DS9 or Voyager and compare them to shows that were on at the same time, they were much more theatrical.