First, it obviously did not matter that this man didn't own a gun... he was still successful in killing another human being. If someone wants to commit a crime bad enough, he will find a way even if it means pulling a spoon out of his kitchen drawer.
Second, if you really want to make a big statement in China it sounds like your biggest opportunity would be to kill a foreigner. Did this man realize these victims were American? Only an investigation will tell (and I hope they will run a full investigation and not just take the word of a few officials). Here's a picture of their daughter (who happened to be with them at the time of attack but luckily not injured). She certainly doesn't look to be a citizen of China, especially with the United States flag on her top.
So what was the point of this attack? Did the man know he was attacking Americans... specifically a family with ties to the Olympics? Was it random... was he plotting to bring attention to his cause (whatever that may be)?