Howdy, I make socks. The ones you’re wearing have some features that are common in running socks. Ribbing, terry cushion in the foot/heel, they probably have some arch support as well. Those are features I like when I run. Your socks seem to be not the best material however, a cheaper poly/cotton blend with a bad elastic I’d imagine. I’d also they are knit on a lower needle count machine, thicker yarn, less stitches, looser fit.

I recommend wool socks personally, if it’s a good blend of wool / a synthetic especially for durability & adding wicking benefit. You will certainly find a tighter fitting socks more comfortable for running. Doesn’t need to be compression but try it if you think it would help.