The Quake II remaster allows you to play with others locally via splitscreen. If you would like to change the way your screen is divided up, then you can check out this tutorial from Seeking Tech.
1. For the first step, you need to make your way over to the Options menu.
If you are currently playing the game, then you need to bring up the Game menu first and then select Options. If you are in the title screen, you can simply select Options from there.
2. Next, you need to select Display.
3. You should see the Split Direction section appear near the top. It should be in between Field of View and Texture Smoothing.
4. By selecting Split Direction, you can choose either Horizontal or Vertical.
Horizontal will split the screen where the top and bottom sides are each dedicated to one player if you are playing a two-player session locally.
The Vertical option will split the screen in a way so that the left and right sides are each dedicated to one player.
The Quake II remaster supports splitscreen support for up to 4 players on the PlayStation 4, PlayStation 5, Xbox One and Nintendo Switch. The PC, Xbox Series S and Xbox Series X versions support up to 8 players when it comes to local play.