Yes it is easy to see that Josh/Rex dont have time for any potty break when he play video games. Thats way i think that he decide to where his cute pink diaper when he play so he does not need to take any breaks to visit the potty. And from the look on this cute drawing he dident even seams to notes that he have end up whit a messy diaper. And way should he think about that? He wear his pink cute diaper for a reason so way should he have any focus or listen to signals from his bladder or rectum now when he wearing a diaper that can handle the accident that he have during the fun play time that he have. This is what diaper is for to handle the accidents that can happens so you can focus on other things and change the diaper when you have the time for it.
I only hope that Josh/Rex dont wait to long so he ends up whit a diaper rash.