Well, I'm simply using multiple samples for the downsampling (like a small blur).

In addition to that I'm applying a bit of sharpening (in this case with a slightly bigger blur radius than the downsampling).
Note that I'm doing it in the same shader. I'm usually not a fan of sharpen filters but it's a different story here since there is a high-res source image.

So.. this isn't really 'fast', but there's room for performance improvements.
For example, using the same samples for the downsampling and sharpening would decrease the number of texture instructions a lot.
Also, using point filtering and then applying a predefined weight to every pixel could be faster, too. (Not sure about that though)

Let me know if you need to know more.

And yeah, the pawns are a bit tall. I didn't make them, though ;P