It's a tough decision to make. Is your child routinely winning Diamond? Is that his rank? Are there any local leagues he can join to pit himself against others?
Gaming is a great hobby unless you are "discovered."
How are his grades? Would they suffer if he dedicated more time to gaming? That would also tell you how much to support it.
Believe it or not, a lot of the guys playing have degrees (college), and are very bright. They are exceptional players, and in most cases, people. If your child can get to that level, I'd root for him. lol