Yeah that song's a good effort, but of course not a scratch on the original; you can't really compete against Ray Charles. I found the same with all of Hugh Laurie's most recent album actually, it was a good effort, but it wasn't authentic and felt more like a tribute or 'covers band' type thing. He's English and white, he'll never quite get the bluesy sound that he's looking for.
Here's some recent stuff (This song is a bit more soul than jazz, but still):
http://www.youtube.com/v/Kmc1XN3iVVcand some not so recent stuff (1944):
http://www.youtube.com/v/TXegyQvEDecAnd something from a true master of the piano, I prefer the original on which only a piano is heard and it's slightly more complex, but sadly youtube doesn't have it, so this will do:
http://www.youtube.com/v/lb84P6gbEYI