Race can be a component, our current group is running as all dwarves and (mostly) playing one of the common dwarven stereotypes.
"You're just going to break in?" said Sacharissa.
"We'll say we were lost," said Boddony.
"Lost underground? Dwarfs?"
"All right, we'll say we're drunk. People will believe that. Okay, lads...."
Another is the gruff dwarven warrior stereotype, and I expect we could all come up with ones for every race.
But the problem with playing stereotypes, is that just that - they're stereotypes. And sticking to them denies a player the chance to do what the game is about - ROLEPLAY. That's the R in RPG after all. I'm having fun playing Alesmiter as a slightly stunned, drunken dwarven bersek cleric, but in another campaign perhaps I'll want to try playing a Casanunda style character who goes against all the dwarven stereotypes.
I don't believe that sticking to stereotypes is what Stelios has in mind in his post, but the alternative isn't clear to me. I'll posit an alternative theory as to why so many characters act alike regardless of their race. To use a delightful phrase I've seen at several other RPG blogs - 'Murder hobos' have more in common with each other than with the people they sprang from. In other words, it's not that they are played like "humans in funny hats", but that they are played like adventurers.