Are you resting your palm on the desk? That's the only way I can think that you might be straining your wrist.
If so...

Ideally, you shouldn't be resting your wrist/palm while typing or gaming. This causes strain as you're describing.
A wrist rest is not the correct solution. These are meant for resting your palms while you are not typing. While typing or gaming, they will restrict your hand movement and possibly cause more strain if your palm remains stationary.
If possible, try moving your keyboard deeper into your desk. This allows you to rest your upper forearm on the edge of the desk and act as a pivot point which should give you the height you need for a proper typing (or gaming) experience.