>Huh? So wanting to get better at side skills in my job makes me a robot?
No, but assuming there's no connection between the company culture and productivity assumes that developers are completely emotionless robots that only focus on skill development because of professionalism.
Of course most developers do somehow proactively try to improve their skill set, but assuming that emotions and psychology don't matter, only salary, is very weird. Developers are often some of the most emotional people I know, they're curious, opinionated, playful etc. This is all from emotions, not from salaries, or purely self-driven. And if you use the innate playfulness and curiosity to improve the team, by creating little games like this, then you are doing one aspect of good management.
Surely it shouldn't be your only management strategy, but nobody implied that.