It's not a totally off-the-wall question, as direction does sometimes matter, e.g., you want your beer to be flowing the opposite direction of your coolant in your counterflow chiller.
The reason it matters for your counterflow chiller is that there's a gradient, or change in properties, along the length of the chiller -- the beer is warmer at the inlet than the outlet, and the coolant is cooler at its inlet than its outlet. Send the beer in the same direction as the coolant, and you have very hot beer next to very cool coolant on one end, and beer and coolant approaching the same temperature on the other, which is a very different scenario than sending them in opposite directions, where you'll have very hot beer next to lukewarm coolant on one end, and sorta warm beer next to very cool coolant on the other.
With your stirrer, there's no gradient in wort temperature as you move around the kettle -- the wort at "twelve o'clock" is the same temperature as the wort at "six o'clock" is the same temperature as the wort as "eight thirteen and seven seconds," so it doesn't matter which way you send it around in. Now, the beer at the top of the kettle is likely to be warmer than beer at the bottom, so, you might get some mileage out of plumbing your chiller such that the cold water starts at the bottom and moves up... but, with the wort being vigorously stirred, it probably doesn't matter much.
TL;DR: it doesn't matter which direction you stir
