You can do it wirelessly, but there are two major issues. First, sharing wirelessly with your Mac requires that you configure sharing as if your Mac was an actual wireless router, including assigning an IP address-but that will produce a problem called "double NAT." That's bad and can keep your game systems from connecting at all. There's also the requirement that your Mac be turned on to make this work, which is a waste of resources.
On the other hand you can use a very inexpensive switch and wires, stick them along the baseboard, and not have them very visible at all.
Your dad probably doesn't have the time to become a whiz at wireless networking, and rather than accept the risk, he's decided to not have a wireless network. That's an intelligent decision. It is actually fairly easy to set things up to have strong security, but it does take some effort and research; you can work on convincing him on this all you want, but it's his decision.