Is This Really About Competition?

This is a study that people are using to suggest that the more competitors there are in a situation, the less competitive people become. Here's the thing; I don't know that what they show means what they say it does. Take a test with 10 people or take it with a thousand people, my desire to do well on the test doesn't change.

But what does happen? With a thousand people there will be many more people needing to go to the bathroom, hungry, thinking about a nasty spat with their significant other, etc... Personally, I don't like crowds, and no doubt there are people for whom such events are terrifying. There are huge effects depending on how the experiment was constructed, but I've seen this study referenced twice already as if were gospel.

How does one construct such an experiment in a way such that competition is the only variable? Perhaps they can make a compelling case that they have. It just seems extremely unlikely.