One thing I know for sure is that chess is the main subject of my daughter's application. She only applied to one top liberal art school, and got in. She was accepted before the NY Times article came out. So I am sure there are some qualities of chess players that the college acceptance officers like.
One character all chess players possess is persistence. To reach some level, no matter it's GM, IM, national master (2200), expert (2000), or class A (1800), the players have to spend 5 to 10 years to study, practice and play in tournaments. There is no shortcut. S/he has to be persistent, maintaining her/his passion, motivation, and interest.
Another character is focus. If a chess player can focus on improving her/his chess, s/he can focus on academics too. Not surprising, s/he often performs well in schools and tests. That's one big difference between chess and video games.
Third character is positive social impact. Not everyone has it, but playing chess definitely helps. S/he has to go to class, go to chess camps, go to tournaments, and interact with other kids. S/he will make friends, join clubs, play as teams, etc. Sooner or later, s/he will consider making contribution back to the society: volunteering, teaching kids and adults chess, and promoting chess among girls and underprivileged.
The last character is the most important, in my opinion, much more important than her/his rating or grade. If your child is weak in this area, s/he should definitely work on it, getting some friends, join clubs and play on some teams.