But hey its a whole building with internet but the download and upload speed are fast enough to play online games right?
Absolutely. Granted, it does depend on where the servers for your games are located. Meaning, you can have the fastest internet in the whole country but if you're trying to connect to a server on the other side of the world you'll still have a low ping and choppy connection.
But, if we're just considering your local network speeds, your setup is just fine