Looks like compression artifacts, which isn't really related to keying. You need to apply a de-blocking plug-in or use the respective manual techniques. The screen color is shifted into the blue, but should be perfectly keyable without oversaturating the color...
What Mylenium said was accurate. You need to reduce the edge artifacts and then use the edge cleaning tools in AE and in Keylight. Every time I'm faced with a shot that has this kind of trouble my first step is to make a 10 bit or better digital intermediate using a production codec or render the original video to a Tiff sequence, then do the rest of the processing on a file that has greater bit depth. You should be able to choke down and refine the edges enough to remove the edge artifacts but you are going to have to settle for losing a little edge detail also.
In the future please drag your sample images into the Reply field on this forum instead of linking them to external hosts. I've almost completely stopped going to external URL's to look at things because if I don't know and can't verify a site I'm not going there ever...
Thank you both for your help.
As recommended, I will drag the photos into the reply field from now on. Sorry about that
Also, can either of you recommend a 'de-blocking plugin'?
I'd think AE's built-in Simple Choker or Matte Choker can do the trick. So would the one in Keylight. When choking, using the bare minimum is best.