When players become engrossed in a game, it is easy to loose track of time, and become oblivious to strain that play might be having on the body.
Injury can result from prolonged play; holding the device in the fingers & thumb for long periods of time, straining the neck and shoulders. Or from rapid & repetitive movements needed to manipulate the console.
These actions, over time, take their toll on the tendons which control the thumb. Most commonly resulting in a condition called DeQuervain's tenosynovitis. The tendons at the base of the thumb become swollen and painful, in sometimes can 'creak' or catch during thumb & wrist movement. The sheath surrounding the tendon can also become swollen. People describe a burning pain over the back of the wrist and thumb, often accompanied by swelling.
Rest is initially recommended to decrease load on the tendons and reduce swelling. Reducing play or taking a break from gaming will almost certainly help. A splint will support and decrease load on the tendons; allowing for healing. Sometimes a cortisone injection or anti inflammatory drugs are recommended. And in some cases surgery will be required to reduce pressure on the tendons.
To prevent Gamer's Thumb, taking regular rest breaks and reducing the time played each session is recommended. Try setting an alarm to remind yourself to stop, rest and stretch- and get in the habit of doing so. Take care of your thumbs, after all, it is said "the thumb is half the hand!"