Your example only talks about the portion of the work devoted to this kind of labor. It also presumes that all other variables remain exactly the same, which isn’t likely. A job that places greater emphasis on social interaction would put you under more emotional stress than one that doesn’t. But so would a job where the customers are shitty and pissed off all the time. Even a job where you never talk to customers, and work with only one other person that you only have to talk to once a week is going to involve ‘emotional labor’. How much labor depends entirely on a huge number of factors, perhaps most importantly your own personality.
The only distinctions I’ve seen in this thread are based on ‘how much’ is involved in a role, or (as per the definition in the parent) how that labor is marketed to others. You could talk about one job involving more ‘emotional labor’ than another, but you’d have to think pretty hard to come up with one that didn’t involve any. Even then, you can really only discuss that on an individual basis. There are some kinds of social interactions that leave me emotionally exhausted, but for other people they may not notice any emotional impact at all. Then there are things I never struggle with at all that I know drive others mad with stress.
The distinction made in the parent comment’s definition is even less sound. Your employer will always have expectations around how you interact socially with the people your work brings you in contact with. Whether your employer chooses to market that as a competitive differentiator has absolutely no bearing on how demanding those expectations are to meet.