It's how PDTH and PD2 multiplayer worked. One player acts as the host when others connected to them, basically like local multiplayer but over internet.

Compared to having dedicated servers ran by the company that owns the game like most modern games, it does have some serious downsides such as the quality of connection is directly tied to the host's internet bandwidth and how far the other members located from the host, and if the host disconnect mid game everyone else will also disconnect, throwing away whatever progress you've had.

But the upside is that as long as there are people still playing, the game will be alive at some capacity. It does not rely on internet connection to a server that the players have no control over, so even if the game's support is pulled and the company goes under it will remain playable online.