Then how can they offer such a deal? Again it's, simple, the quality will suffer dramatically. You will lose connections, lose game states and have low FPS. (You can find plenty honest reviews stating this).
Having said that, we aim for customers who are willing to pay a fair price for an awesome game experience. Our current price is $9.99/4 players/month which translates to $2.5/player/month. Seems fair to me...
Even if they are using AWS (which personally seems like a poor decision for this kind of use case), I don't think your pricing comparison is fair. On demand pricing is the most expensive way to rent AWS servers. Reserved instances, dedicated hosts, and savings plans can cut the cost you quoted by ~70%. By your calculations that's 100 players for ~$33/month.
Owning hardware does not make it necessarily cheaper. Most often to the contrary.
So by your approximation they still make -$23/month?
Either way, we offer a solid Factorio Server Hosting Service, where you do not have to bother with capacity limitations, resulting lags or an awful configuration panel. We solve this problems and we offer it for $2.5/player/month. If you want a smooth gaming experience when coming home from a stressful workday, we are the right choice. If you dont care for about the aspects mentioned above and you want to pay a few cents less per month, you should probably us a different game server host.
Our focus is quality of service.