If you continue with the idea that lowering stress during the fighting of an infection would be able to reduce the duration or length of the infection, and possibly reduce the symptoms, watching a movie or listening to music you enjoy is likely to heal you faster than something not enjoyable like staring at a wall. This may seem like an outrageous comparison, but note that a doctor's office wall that may have been bare years ago probably has a conscious design of color or artwork. By removing the sterility of the office, the person may be put in a better mood, leading to the potential for better health.
Would playing a game on your handheld device improve your mood and wellbeing more than just checking the weather or reading news? I feel it is likely to do these things. Believing a game can improve health leads to the next concept. Can a game be designed to be more healing than another game? if a movie can be more enjoyable than another movie, make you laugh or smile more than another movie, wouldn't the more enjoyable movie make you feel better? A similar concept is taking to a friend. Would you feel better talking to a friend with a good connection and rapport versus a person you lack a connection with?
If a movie can be more enjoyable than another movie, or talking to one friend can be more enjoyable than taking to another friend, there is no reason to believe a video game cannot be designed to be more healing than another one. But just as talk therapy or cognitive behavioral therapy can be designed to be healing, a video game should be able to be designed to be healing as long as one specific condition is met: the video game does not result in above-optimal health.
In most people, we would consider it abnormal to believe that their health could be above optimal, more than 100% of its potential. But the human body is not perfect, and it is possible to have scenarios where a body tries to, and may accomplish, doing more than it is intended to safely do. This brings us to the argument that some "games" would have to be restricted by age or require a prescription. (I had a friend note than standard drug laws may not apply because the game does not have a physically ingested element or physical hardware element, which may allow therapists to prescribe the game. A therapist is also likely to be able to better recommend a game title because of their increased investment in a patient's individual issues.)