How to make plastic badges?
What you are seeing may have been constructed at the gym, but they would have used a device available to anyone. It's likely called a badge laminating machine or some combination of those terms.

Amazon sells a number of designs encompassing various size capacities.


This is just one of many available. This particular model has a production restriction in that you cannot produce too many in too short of a period. If you exceed the limit, it's likely the machine will overheat and damage something internally.

More expensive models will have higher production capacity.