Storing no of players the last seven days in an online game
I would store the timestamp, server identifier, and number of players in just the way you thought of, deleting the oldest (if you need to) and adding new ones every 15 minutes.

Moving the server names into another "server" table and referencing the primary key in your player count table would be a more conventional normalised design.

With reference to the trigger, don't forget that you can perform both the insert and the delete in the same SQL statement with a common table expression: http://sqlfiddle.com/#!1/c8362/5