This is just what you think it is: a pre-Trek, pre-Captain Kirk William Shatner, he who appeared on various popular SF (or sci-fi or whatever they call it now) TV shows of the mid-'60s. I believe this one was The Outer Limits. He also did a couple of turns on The Twilight Zone, the monster-on-the-airplane-wing one and another one, much more low-key, in which he became addicted to a sort of Satanic coin bank that was foretelling his death. Jeffrey Hunter,the original Captain Kirk in the failed pilot, didn't seem to have this paranormal/space epic background, or if he did I don't remember it. He was in Biblical movies, I think, and didn't know how to do that infamous wrestling throw that bested Kirk's worst enemy, the Gorn. He was just too bland, and what they seemed to need on the show was the sort of histrionic performance that led to his deathless soliloquy: "No blah-blah-blah!"
Which see.
But wait, there's more! Leonard Nimoy also did at least one turn on The Outer Limits (that I know of - he may have done some Zone/One Step Beyond as well. He had a family to support.) It's eerie how similar this shot is: both of them looking at something disturbing on a screen, though Nimoy turns away with a mildly perplexed look on his face and Shatner looks as if he needs a Pepto-Bismol. Though these appearances weren't on the same episode, guess what! . . .
They appeared together on The Man from U.N.C.L.E. in 1964. I probably watched this episode, since I was slavishly devoted to the show (and unlike all my friends, I liked Robert Vaughn rather than David McCallum). Like everyone else, I had no idea these two journeyman actors would become cultural icons, and neither did they. All in a day's work.