When you launch this map normally, then you will see only two options: Custom, Wingman.
To play the map in other gamemodes, simply copy the console command without changing it. Console commands are in the quotation marks.

Casual: "game_type 0 ; game_mode 0 ; map_workshop 3071005299 de_assembly"
Competitive: "game_type 0 ; game_mode 1 ; map_workshop 3071005299 de_assembly"
Wingman: "game_type 0 ; game_mode 2 ; map_workshop 3071005299 de_assembly"
Training Day: "game_type 0 ; game_mode 4 ; map_workshop 3071005299 de_assembly"
Arms Race: "game_type 1 ; game_mode 0 ; map_workshop 3071005299 de_assembly"
Demolition (Half broken) "game_type 1 ; game_mode 1 ; map_workshop 3071005299 de_assembly"
Deathmatch: "game_type 1 ; game_mode 2 ; map_workshop 3071005299 de_assembly"
Custom: "game_type 3 ; game_mode 0 ; map_workshop 3071005299 de_assembly"

There aren't any more accessible gamemodes. If there will, I will update the discussion if I can

Edit 1: you can find gamemode list here https://developer.valvesoftware.com/wiki/Counter-Strike:_Global_Offensive/Game_Modes