I found a few things online myself too, while not specific to gaming chairs/bonded leather there are a few about getting puke smell out of leather car seats. Seems that the puke can seep through the seem into the cushion and get trapped there.
I really don't want to resort to vinegar as it smells almost as bad as the puke does.
They suggset sprinkling baking soda on the seat and seams and letting it sit for a few hours before vaccuming it up. This is what I am currently trying.
Just have to make sure Kabuto stays off or he will be pure white instead of black and white.