I'm surprised that it ended up going off of the left hand side of the runway with a cross-wind from the right. In most aeroplanes the weather-cocking effect of the tail and aft-fuselage ought have promoted a swing to the right as the rudder (full left in this case to keep straight) loses effectiveness as you slow down.......
By the time the rudder loses effectiveness, surely the nosewheel steering will keep you from exiting
into wind...