ZDoom

You can't. The software line drawing function has no switch for that.

Unfortunately that cvar doesn't exist on Linux since that's part of the d3d9 renderer.

So... how would I go about doing the same here?

I didn't know about that cvar! It wasn't in the automap settings menu (at least, I don't think). Thank you.

The lines are antialiased. If you don't like it, set vid_hwaalines to false.

I guess there's no option to disable antialiasing on automap lines?

In ZDoom, the lines on the automap are very blurry when viewed in lower resolutions. This is in contrast to Chocolate Doom (and by extension, Vanilla Doom itself), where the lines are sharp. This becomes especially apparent if you zoom out in a large map.

Both screenshots below were taken at 320x200 resolution, scaled 3x (click them for their full size). The command line parameter "-4 -width 320 -height 200" was used for ZDoom.

Chocolate Doom:
[attachment=0]LowResAutomap_1.png[/attachment]

ZDoom:
[attachment=1]LowResAutomap_2.png[/attachment]