job related to game physics

[s]Well, there aren't many jobs related to game physics to be honest. Game physics is continuously improving, but there aren't any major leaps , compared to e.g. rendering. There are some good, even some free, physics engine avaiable and creating a physics engine, a stable physics engine ,is incredible hard. Therefore most, if not all, studios uses one of this engines.

Mathematics is getting more and more important in rendering (but this market is already ruled by existing professional engines too).[/s]

Okaay... sorry for getting Off Topic

What about other side-skills?

Well, soft skills are useful.

How much should I know about graphics programming, and to what extent should I know DirectX/OpenGL?
What about networking?
What about other side-skills?

I'm a graphics programmer, but have worked with physics programmers.
Knowing enough of a graphics API (of any kind) so that you're comfortable with drawing debug shapes (e.g. visual versions of your physics capsules/boxes/spheres, or force lines, arrows, etc) would be handy. Also, knowing how to transfer object transform data (e.g. a 4x4 matrix) from your physics engine over to the visual objects.
You'd almost always be doing this via a higher-level graphics engine, not D3D/GL directly, so learning those APIs specifically isn't a strict requirement.
Perhaps if you were doing something more advanced, like soft-body simulation, or CFD/Navier–Stokes equations, etc, then you'd want to have a much better grasp on graphics and visualisation techniques.

If you knew enough about networking to be able to have a conversation about how to handle the network-replication of physics-driven objects, and different networking strategies, like dependent lock-stepping, authoritative servers, etc, then that would be a plus.

Being qualified in another role -- either general gameplay programming, and/or another speciality like animation systems, would be very useful.
As mentioned in the off-topic above, (almost) everyone uses existing physics engines, so the job of the physics programmer is to tame that existing code and make it do exactly what a specific game requires -- this might not keep you busy for a whole project, so being able to perform other roles might be required of you.

As for educational materials, I always see the same few books on people's desks.

Shell scripting. Whether that be bash script, powershell, or something a little more friendly like Python, is up to you. But either way, you need to know your way around the shell (find, grep, sed, etc.), and know how to write scripts to automate repetitive tasks.

Could you name an example specific to physics programming where shell scripting is used? I've heard of shell scripting before, but that's about it.

I was more intending that as a general injunction towards any form of programming. A programmer who doesn't know their way around the shell, or can't automate simple tasks, is a pretty useless programmer in most environments.

Also, physicists love python.

I just don't know my way around the shell... Is that a problem?

It's not necessarily a deal breaker, but it's definitely something I consider a deficiency in any serious developer.

What happens when you need to search for a specific pattern in 500 MB of build log files stored on a remote build server? For a someone familiar with the command line thats a one-line call to ssh+grep. If you are stuck in GUI-land, it's likely to present a stumbling block...