That gray rectangle with two red buttons is a gaming relic. Modern controllers require the player to combine a sweeping legato — two analog sticks, one controlling a character’s head and one its feet, are used simultaneously — with the precise staccato of four buttons, two triggers and two bumpers.

It can be challenging, and especially so for those with physical disabilities. Some e-sports competitors have operated controllers with their lips and chin, or their cheek and tongue. Ms. Hawley, 35, cannot use her index finger to pull the right trigger on the traditional Xbox controller.

Instead she can press an elbow against one of the two four-inch buttons on the adaptive controller, which she tested for Microsoft and which has resurrected a pastime. She now plays games like Mortal Kombat and Kingdom Hearts with her brother and her niece every Sunday.

The power of the adaptive controller stems from its 19 3.5-millimeter input jacks and two USB ports, which enable users to plug in peripherals like external switches and buttons. Many players share intel about setups to accommodate specific physical needs.