It really depends on how far away from the data center you are. I used to live close to Amsterdam and that felt basically local, even with a not-amazing internet connection. Right now I live in the Valencia (Spain), with a local and not very well paired ISP. There is lag, but it is just about acceptable for platformers and action/adventure games. I wouldn't recommend it for shooters.

The cost ended up being around 1€/hr when the instance was on, and 0.06€/day for the storage. I am sure this could be optimized (e.g. use snapshots and spot instance) - but I just couldn't be bothered to. For me it is worth it.