I’ll assume that was the pilot. I’m used to these uniforms:
No, that's later. The pilot "The Cage" was with Captain Christopher Pike. It later became "The Menagerie" when Star Trek was eventually picked up and they needed something to fill up the season.
Here are examples of the officers uniforms, crewmen and outdoor gear. The daily uniforms are similar but different. Sort of like TNG to later DS9 diferences. It just seems appropriate that if the Captain is Pike. They'd wear Pike era uniforms.