If they are serious about it I would let them, since being a professional gamer can make some good money with the rise of more competitive games being released lately.
If they also wanted to they could become a YouTube commentator and could possibly make money from there as well if they are unable to become a professional gamer.
Let us say the average per thousand views is $2, and a decent Youtube commentator with a few hundred to 1000 video would get around 500,000 views a month. That would get you about $1,000 a month, and about $12,000 a year.
However YouTube video game commentators with several thousand videos tend to get anywhere from 1,000,000 - 4,000,000 views a month which would be $2,000 to $8,000 a month. Which would get you about $24,000 to $96,000 a year. If you are dedicated and provide decent, useful or unique content, and update frequently you could make a pretty good income gaming.