If you want timber, yes...you want it to grow up taller. Thinning will increase crown size, but a wider crown will give you more acorns, so if wildlife is your goal, that is good. That tree is never going to make a good log. If there are relatively few oaks in the woods, I would open it up. Cut at least enough so that no other tree is touching the canopy of that tree. Then look around and see if there are other junk trees on the edges of the circle you just made and cut those too. I'd even consider fencing a small area to keep the giant rats (oops, deer) out so seedlings stand a fighting chance. Maybe draw a big circle around it and divide it like a pie...fence off 1/4 until the trees are 8-10' tall then move the fence to another quarter.
You aren't going to get a great corn crop in partial shade, but there are some clovers that do really well in an area like that so selecting the right mix for the food plot makes a difference. If you want a bigger area, measure the height of of surrounding trees and open an area at least 2x the diameter of that height (for example, if trees are 75' tall, make a 150' diameter circle where you cut everything over 1" in diameter). I would leave any oaks in that opening if it were me.