I have no idea about "legal" or not. But, I wouldn't go with those for a few reasons...
1) They look to be very bulky. Our coach prefers socks to be thin and stretchy so the foot shape can be seen easily. Bulky cotton bits at the toe could get him a deduction for unpointed toes.
2) The boys don't really need "traction" so to speak. They are really only starting from and landing on socked feet. Their feet will otherwise be up in the air. They need to be able to stick the landing, but if they shouldn't need to rely on sticky socks to do it.
3) The bottoms of the sock will get a little dirty during competition. (Some gyms are worse than others.) I imagine that the white lettering on slightly dirty cotton might be distracting to a judge.
Finding good white meet socks is a bit of an art form. If your gymnast's feet are big enough (US boys size 3 or 4+) you can find nice thin white socks in the womens' section of Target or Walmart. If his feet are smaller, then it gets tricky. (I am still mad at Sports Authority for discontinuing the *perfect* sock they used to make last year.) This year I found a good multipack (4 white pairs, 4 other colors) of no-show Danskin Now socks in the girls section of Walmart. We are also trying some quarter-height socks I found at Costco in a multi-pack of half black and half white.
That was way too much, wasn't it? Seriously, I could write a manifesto on finding the perfect white meet sock.