Tiger Woods is an elite athlete and Golf is a sport. Are all golfers elite athletes though? Hell no.
Tiger is definitely an elite athlete and I did vote for Golf being a sport- it may not require super athletic skills(see John Daly puffin' and drinkin') or an athletic physique(see Phil Mickelson's glorious man-boobs) but the mental toughness, practice of long hours honing different shots with different clubs and the maintenance of your body to remain strong and flexible. A lot of golfers did not work out until Tiger came onto the scene and his driving length forced them to adapt their game(and physical abilities) to try and catch up with him.
You can also see Tiger's development and changed swing- back when he first entered the PGA the announcers would talk about his crazy body torque on his drives, knowing that over time that would put to much stress on his low back and knees he adapted his swing. Now it's tighter and puts less stress on his body. Tiger is definitely an elite athlete.