Tournament Mode is not in the demo v0.8. It is a feature of the full version (v1.0+ / Beta / Current) only.
Not built-in. Community runs tournaments via Discord (SSF2 Community) + Parsec / Slippi (for Melee) / direct IP. Join discord.gg/ssf2 for events.
Demo v0.8 is a 2011 time capsule. Get the full game for Tournament and everything else.