I worked for the company that made the Vetrex in the mid 90's. By that time they'd become the company for bowling and similar physics based games. Jay Smith, owner of the company, wrote all the physics sims himself, in Excel, which we the programmers translated to C.

My guess is the same way color raster CRTs work: there's an aperture grille or shadow mask and three electron guns, and the grille masks off the beam of each gun except for where it's supposed to hit its corresponding color phosphors. Color mixing is performed by tracing over the same vector lines with more than one gun.

If you look carefully at a Star Wars arcade machine, you can see the shadow mask in the vector lines. You cannot see this on, say, an Asteroids machine or a Vectrex; on those, the lines are smooth and sharper than a draftsman's straightedge.

Everyone should experience an original Asteroids, or failing that something like the Vectrex, at least once in their lives. It's indescribably different from emulation; the long-decay phosphor and direct CPU control over brightness means that shots and explosions glitter in the dark in a way not even MAME can replicate.

Another anecdote about the original Asteroids machines- the dynamic brightness of the vector displays added a great effect: the asteroids themselves were sort of grayish lines with very sharp, crisp edges, but shots fired from alien spaceships were searingly bright, and would and up also exciting the phoshor around the shot itself, lending a bit of a halo effect.

Jed Margolin, Atari engineer, wrote the ultimate papers on how the Atari vector games worked. These two pieces are excellent reading when you have the time:

The Secret Life of XY Monitors : http://jedmargolin.com/xy/xymons.htm

The Secret Life of Vector Generators : http://jedmargolin.com/vgens/vgmenu.htm

The first covers how the tube worked, the second covers how the Atari systems generated the graphics to show on-screen.

Also the Retro Game Mechanics Explained channel on YouTube has a very well put together video about this as well:

https://youtu.be/smStEPSRKBs

This slow mo video of a vector graphics arcade machine recently introduced me to this technology - I was a bit too young to actually be there in person, so never realized that this kind of CRT (?) drawing technology even existed.

https://www.youtube.com/watch?v=eJVpYL44jUQ

Friend of mine that I worked with had a Vectrex! I was also blown away seeing this, it was such a neat machine. That was back in the day when video game systems hum was a definitive part of the experience.

I'm too young to have used a Vectrex, but I like this demo that it inspired:

VX2 by Spectrals https://www.pouet.net/prod.php?which=85304