I was confused by Taelan28's explanation of how slalom skiing isn't physically demanding until I read his thread about help threading the gates. If you are a free skier, and there is nothing wrong with free skiing, then the physical demand on your body is completely relative. Not to mention if I was skiing behind an outboard with no speed control, well that might barely constitute slalom skiing at all. You get behind a 350 hp malibu with zero off going 36 mph and pull out for the gates at 38 off or shorter and know you're in for the hardest 16.08 seconds of your day and fight for every buoy then tell me it's not physically demanding.
I'll even use your definition: Physically demanding requires strength, speed, stamina, agility and a range of motions. If this doesn't define your style of skiing then you might want to stick with rock climbing because you're involved with recreational skiing not competitive slalom skiing.