How am I supposed to arrive at the conclusion that my video driver is called "intel"?

Normally if you install "all" X11 video drivers and start X11 the first time it will try to autodetect which driver it has to use (see this other question for an example). See also this explanation (that is not specific to ArchLinux) : https://wiki.archlinux.org/index.php/Xorg#Driver_installation

It seems like based on don's input, I need to look in the Xorg log. The problem is that with Xorg, you need to know the driver group in advance or install all drivers as Patrick Mevzek suggested.

Only then can you identify the "intel" driver specifically.

Searching for the words "Module" and "driver" and then reading the surrounding lines seems to do the trick (including the full log). My strategy was to search for "Module class" and look for: "X.Org Video Driver"

cat /var/log/Xorg.0.log | grep 'Module class' -B4 -A4

Relevant Lines

See LoadModule: "intel"

[  1065.037] (II) LoadModule: "intel"
[  1065.037] (II) Loading /usr/lib/xorg/modules/drivers/intel_drv.so
[  1065.037] (II) Module intel: vendor="X.Org Foundation"
[  1065.037]    compiled for 1.19.0, module version = 2.99.917
[  1065.037]    Module class: X.Org Video Driver