It specifically says you are responsible for all fees associated with using AWS.
I recall the horrific fad maybe ten years ago of forcing "employees" to come in and work on their free time for hackathon and maker type events to generate corporate PR. Perhaps, this "Personal Game" policy is a legacy from some awful corporate hackathon event from back in 2012 that nobody even remembers anymore, but the legal paperwork remains in the air like a bad smell.
I suppose until the censorship is removed and we find out the precise legal definition of "Personal Game" we can only wonder and do the usual "big company always bad" thing.
We should assume good faith on the part of James Liu and Robert Adams unless you have evidence to the contrary.
To your point about carrot and stick - yes, the carrot here is likely excellent financial compensation for doing the main job, and the experience on the resume, same as all your colleagues. Amazon aren't going to pay you extra because your hobbies are impacted by their policy - at junior to mid levels it's take it or leave it.