The ESPN Club does not take PS.
This isn't to make it hard on guests, but rather to make it less frustrating -- on big game days (especially weekends during College and Pro football), it is absolutely impossible to gauge how many people will come in and how long they will stay. Other restaurants, because they're not sports-oriented, can estimate how long their guests will usually take to eat a meal and can formulate PS times off of that.
At ESPN, it's always unpredictable. Because there are no rules on how long you can stay at a table, it's not unheard of for people to come in at 11:00 AM for a Sunday night football game. The Monday Night Football crowd will almost always show up a few hours early. Because you can't predict what will happen and what games will be huge (it not only depends on the games, teams and the team rankings, but everything else, too, including where your guests are coming from -- I remember more than one night where there would be a LARGE group clamoring to watch some D-1AA basketball matchup the rest of the country would deem largely irrelevant.), using the Priority Seating program would just frustrate everyone -- guests and CMs alike.
ESPN is the only Disney-owned restaurant on property that I know of, though, that does not accept priority seatings.