People who comment on the internet are amazed by this swimmer. "Can't handle" is like saying you can't believe it, but it's not taken literally. If I say "I can't believe it!" I probably CAN believe whatever it is, I just think it's surprising, amazing or shocking. So "can't handle" is a way of explaining their reaction to what they've read. The verb "to handle" means to be able to hold it in your hands, but it's not used literally here.

to handle = to deal with = to manage = to cope with

Can't handle something means it is too much for your brain to process. As if you can't even begin to grasp it. For example, if a mom has a super crazy and bad behaved child and she doesn't know how to control him she could say "I can't handle him right now" It's used when something is out of your abilities, it's too much right now. The news article is using it in a lighter sense that China's Olympic Swimmer's bodies are so hot that the internet can not manage containing itself. So basically everyone online is freaking out and talking about China's swimmers. I hope this helps!