Yes, it's possible. To be honest, I find it very sad that we have grown so dependent on ISP and big telecom companies to have a working network.
In theory, you could have an infrastructure in your neighborhood and be able to play Quake with your neighbors without making use of the phone line at all, completely free of monthly fees and with a very efficient and fast connection too! you'd just need cabling connecting the apartments/houses and some decent routers controlling/restricting access on each subnet. It's a pity that's not a standard thing when designing residences.
Though less efficient and more limited in range, you can technically do it with Wifi and mesh networking too... there are projects like B.A.T.M.A.N (https://www.open-mesh.org/), however, it's not very user-friendly to set up. I believe there have been some projects that attempted to launch embedded devices to act as mini routers for this, but the spread has not been wide enough to make it worth it, sadly.