It’s been a few years but I think Tarkin introduces Vader a few moments before the choke to the admiral (Motti is the name, BTW)

Even if he knew of Vader, knew of the force, he still didn’t really believe in it. If not shown to someone it is incredibly unbelievable. He definitely didn’t believe in the force being stronger than the death star, which was voiced and angered Darth Vader resulting in the choke.

Also, Motti was a pretty cool character. From the linked fandom page:

Whatever conclusions you ultimately draw about the incident taking place between myself and Lord Vader during yesterday morning’s briefing, he was wrong, and trying to crush someone else’s windpipe doesn’t make you any less wrong, if you’re wrong to begin with. Which he was. I do not concede the argument.