Attaching the thread in reference: https://sports.stackexchange.com/a/3333
You are correct in flagging. As a result of this meta question, the mitigation plan will be to remove these "too chatty" and "not constructive" comments approximately a week after they are made.
Here is my ongoing concern: Sports SE and its community has been recently described as negative (Jon Ericson: "I'm curious why the on-topic page seems so... negative.") and stubborn. Whether justified or not, this has been brought up as an issue.
The user in the thread is: 1) a new Sports SE user and 2) appreciative of the answer he was given. Who are we to alienate our users for saying "thank you," especially if he was adequately helped out? If it becomes excessive, then we can direct the user to our commenting privileges and/or our chatroom.
I much rather encourage "good sportsmanship" than to immediately shoot it down. Given the criticisms Sports SE have received, isn't flagging such comments contradictory to welcoming our users? Again, flagging is the way to go and such comments will be eliminated in approximately a week.