He doesn't get my respect for it, especially if he does it more than once. It means he failed as a leader to get people to do their job, or even to have someone to do that job.
Sometimes, it's necessary to roll up your sleeves and get some work done, but if you are doing other peoples' jobs, it means you aren't doing your own.
His CEO is showing by example what he expects of his employees - if you see something needs doing, even if it's not "your job", then roll up your sleeves and get it done.
No, it means he's trying to get people to do their job and take pride. He's not failed, he just hasn't yet succeeded completely.
I agree that it's a public shaming if he does it right in front of everyone else, but sometimes you just have to buckle down and do what has to be done, even if the work is perceived to be below your station. Obviously work should be invested in hiring a permanent dishwasher, but it is conceivable that occasionally you may not be able to find one, especially if you're intent on abiding immigration laws.