PC copies of Streets of Rage 4 purchased from GOG.com do not support online multiplayer, despite being priced the same as the Steam version that does feature online capabilities.
Our Streets of Rage 4 review says it’s worth checking out, too, even if it prioritises nostalgia over modern advancements.
Streets of Rage 4 is also available on console without these issues, should you be looking for a more straightforward approach to multiplayer.
While that note claims there is no online mode “at this time”, a tweet from developer Lizardcube suggests that online won’t be coming to the GOG version of the game.