From Photoshop FAQ here you can see that:
Does Photoshop take advantage of more than one graphics processor or
graphics card?
Photoshop currently doesn't take advantage of more than one graphics
processor. Using two graphics cards does not enhance Photoshop's
performance.
Multiple graphics cards with conflicting drivers can cause problems
with graphics processor accelerated features in Photoshop.
For best results, connect two (or more) monitors into one graphics
card.
If you have to use more than one graphics card, make sure that they
are the same make and model. Otherwise, crashes and other problems can
occur in Photoshop.
And here there is troubleshooter for graphic cards problems, but the recommended approach is to disable the less powerful card and work with just one.
And too, in the list of the unsupported graphic cards you can see:
Unsupported card series
The following card series are no longer being tested and are not
officially supported in Photoshop:
AMD/ATI 100, 200, 3000, and 4000 series
nVidia GeForce 7000, 8000, 9000, 100, 200, 300 series
Older Intel® HD Graphics (for example 2000, 3000, 4000 series) cards
Some GL functionality may be available for these cards, but newer
features won't work.
Your intel (default) graphic card is unsupported, so, no game for you.