It really depends the game and how developers pogram the game, I did a research about this when I was at university for data science or something like that because I took as an exaple Epic, they have their servers with Amazon, for video games there are a few things to consider from the sever and the game.
From the server where is located, how responsive is and the load that can handle, is only for a single region or do you have more in other regions or countries. Previously spygames did this and since that was sold by Mr.Epic SEO and friends and that project died for the greed of a company and dumb IGN this is important for the second part because....
Now second part to consider the game, some developers add certain load to the server or leave it to be handle by the PC users example multiplayer games where enemies and players can body block means everything is handle by the server how big the map will be and how much stress a single game will put to the server, multiplayer games where there is no body collition most of the process is handle by user PC because server doesn't have to be checking every second the geometry and compare everything to make sure, location, distance and speed of the user is correct and valid also for security if PC user handle the load it means that someone could get that info, your IP, location and use hacks without any poblem since server handle minimun verification.
Now that being said all games now have collition and everything is handle by the server, following Epic they changed so many times how building worked because people was building and editing so fast that server couldn't update, location, position and speed, basic calculations of the game and now imagine that for 100 different matches with 100 players on each match so server needs to go back and for everytime receiving the infor and returning the value to user on his PC.
After telling you so many lies, is not good unless you aim for no demanding games minecraft is really demanding so don't even say it because of the low textures that is loaded on user side no server and the math behind the auto generation is huge!!! so if you want to use your server I will recommend it for mobile games, data transfer and verification shouldn't be huge still depend on how much calculations or updateds the server needs to make to keep updated and what the player sees in real time but with your server I believe mobile is the best option if you want to put it on action, this is my opinion someone else could say I'm wrong because everything depends on the type of game.
Sorry for writing tooooooo much and I almost forgot, security and data integrity, in case of server problems how fast can be fix, replaced and if can continue working after any type of natural disaster, there are standars and verifications that companies look at the moment to choose servers and make sure that under any situation the server never stops, redundacy and backup servers so many things to check I know but big companies will ask for this, indie developers will go cheap but still will request you so many things because is their work in your hands and they want a garantee server will always be up regardles if is small or big company.
There are so many requirements, will be difficult because you are fighting with companies that have years of experience and credibility on this field and high tech equipment, on the other side cloud services for small and local companies is other option, processing power won't be so high.
Well I hope all the previous info help you at least you can have an idea what search and what to take in consideration if you go for gaming server, search for indie developers that is my advice if you still want to go for gaming but test carefully and really good everything to make sure you can get a good deal and you can get your income if you already know everything sorry but gaming industry is wild.
