There is no right or wrong when it comes to if you shall use an game enginge or not, maybe you are better of with something inbetween like for example Pixi.
Code your way to the top of.
Engage in battles with other holes in the same city.
» If an enemy touches your hexar line, you lose.
There are many tutorioals on how to validate a user on the backend using a token.
The server will then find the client in the database and compare the new score to the old highscore, if the new score is higher it will be stored to the database.