Elliptical orbits are in Space-Engine. It's only the very highly eccentric ones (like, e>>0.1) that were removed, and I think this is only temporary until they can be implemented without producing crossing orbits. As for figure-8 orbits and other more bizarre types, although they are valid solutions to gravitationally interacting particles, these solutions assume that there is only 3-body interaction. They are violently unstable in n-body interaction, and so you will never see them in nature. Hence they should not be in SE.
You can still have interesting orbits in n-body dynamics though, such as Horseshoe orbits for co-orbiting bodies, or precessing and zoom-whirl orbits in strongly curved space-time. And then there are orbits in Kerr space-time (near rotating black holes) that are absolutely bonkers.
I never even considered the fact that orbits don't have to be circular.
You mean elliptical? Not even Earth's orbit is circular.