You can change the gamemode on your server on by using the following rcon commands:

rcon_password "yourRconPassword";
rcon game_mode 1;
rcon game_type 0;
rcon exec gamemode_competitive;
rcon mp_restartgame 1;

If you are adding this to the server.cfg via the web console you do not need the rcon part before each command and therefore it would be:

game_mode 1; 
game_type 0; 
exec gamemode_competitive;


For a list of the gamemodes/gametypes to configure your server to the disired mode please see below:

 

Mode  game_type  game_mode
Classic Casual 0 0
Classic Competitive 0 1
Arms Race  1 0
Demolition  1 1
Deathmatch 1 2