there is a lot of play where the hook hooks onto my Hookeroon,, and one of my log jacks also, doesn't seem to be a problem
My log rite has some hook play, but I think it helps since not all of the faces are clean and square. You can torque the nut and boot down, eliminating play but it doesn't move freely. I have seen the log jack sir saws a lot has. Pretty sweet setup
I have the same peavey from TSC it makes a big difference in rolling logs around and lifting them to keep the saw out of the dirt. I think the play in the hook and foot is helpful for work on rough ground.