I have a feeling that you only mention "service" because on Windows it's possible to configure a service to auto-restart when it crashes. I even think it wouldn't be easy to make an arbitrary "game application" to work as a service on Windows because services run with limited privileges.
If you need a script which auto-restarts an application if the latter exits with a non-zero error code (i.e. when it crashes), check Anycorn's answer to a similar question on stackoverflow. It's very simple and it does not involve any services.
If you want step-by-step instructions, here what I would do:
create a directory called bin in your home folder:
create a script "startgame" in that directory:
open it in a text editor:
enter the following text:
while [ 1 ]; do /path/to/game/executable && break; done
save the file;
set executable bit on it:
chmod +x ~/bin/startgame
execute the script by typing in the terminal
All of the above can be achieved without terminal - i.e. create a folder using Nautilus, create a file, make it executable; create a desktop shortcut etc.
If you're interested how the script works:
while [ 1 ]; do ... done
is an infinite loop
starts the application and waits for it to finish (obvously, you need to change it to the actual path of your application)
command1 && command2
executes command1 and then executes command2 only if command1 terminated with a zero return code (which indicates success). I.e. the loop will only stop ('break' statement) if the program terminated without an error, otherwise it'll be restarted.