Interesting. Lots of questions come to mind from that post but I will just stick to your question. While I seriously doubt there is a medical condition that creates an urge to frequent only convenience stores, there is a possibility it could be a byproduct of a well known mental condition. Obsessive compulsiveness can take many many different forms and, I think, could be a reasonable explanation for frequenting convenience stores. To be considered an obsessive compulsive disorder (ocd), it would have to be an uncontrollable urge that the person knows is strange and unnecessary but feels they are unable to get on with their day until they satisfy it.
Ocd can take many different forms and have many different degrees of severity. A minor example could be someone who cracks the knuckles of one hand but cannot fight the urge to crack the knuckles of the other hand, even if they don't feel like they need to be cracked. Some people feel like to just do one hand would make the other "jealous" so they must do the other one.
A major example could be someone who is obsessive about many things - such as making sure all the fringe on an oriental rug is perfectly straight or washing their hands everytime they touch something or even leaving for work but having to come back inside 10 or 15 times to make sure the coffee pot is turned off.
As long as the obsession doesn't interfere with a person's daily life or consume all of one's time such that they are unable to work or have a normal life, it is sometimes best to chalk it up to being that particular person's little tic. Everyone has a little tic - something that is just a part of them, the only difference is that it doesn't consume their life. Mine is even if I know I already set the alarm clock, once I get into bed I have to get out just one more time and make sure it is turned on. I only do it once, but I do it every single night and I can't sleep unless I check. Everyone is crazy in their own right, but maybe that makes being a little crazy actually normal