@commands.command()
async def gameinfo(self, ctx):
game_list = []
for member in ctx.guild.members:
game_list += member.activities
print(game_list['Game name'])
[<CustomActivity name='беги' emoji=None>, <Game name='Visual Studio Code'>]
activities = sum([], (member.activities for member in ctx.guild.members))
game_names = [item.name for item in activities if instanceof(item, discord.Game)]
#если нужно только уникальные:
game_names = set(game_names)