Really? I'm not a programmer so won't argue to the contrary if you know perhaps your stuff better, but I was fairly certain that the two are most definitely connected, and many times in the past developments, devs were switching engines or limiting planned features of their games, based on exactly that - engine limitation. I don't think it's purely graphics related.
You're half-right: an engine (nowadays) as a term refers to far more than just the graphics-related stuff. The persistence (if you, for example, would refer to chasing NPCs respawning with full health when you jump) is about the way the networking works, and what is stored or not, and if so where. The way terms are linked is not universal though. CryEngine, for example, is pretty universally regarded as a
terrible engine to modify. It does a number of things extremely well, but adding things to it or modifying certain aspects is not nearly as easy as one would expect. Especially with earlier versions getting some kind of networking going for example was not easy at all compared with the comparable UE of the time. Cobra seems the other end of the spectrum; while not nearly as 'flashy', it appears (it is a closed platform, so its from what I can gather) very
flexible. Them using versions of it for games like PC/JWE/PZ, games on a totally different scale (ED) and even FPS (The Outsider) is a testament to that.
Do note that while info on CE, UE, Unity and such is easy to come by, far less is known by Cobra as it is developed in-house. So take what I and others say about it with a pinch of salt, as only FD truly knows its capabilities and limitations. The general notion of changing from Cobra to UE is definitely silly though, as the way Cobra deals with scale is something that would take a LONG time to translate to what UE does out of the box. It would also mean that nothing they did with any of their other games would translate as well. To end somewhat unrelated: it is AMAZING what modern game engines can do, and I love what Unreal Engine is able to do.
Of course, getting anything like that in an actual game, using UE or any other engine, is something for the future. What many don't fully realize is that the present is 'disappointing' not because the industry cant do better, but because the target audience can't run what is possible.

Look at the minimum specs of ED on PC, and you'll see just how incredible old the hardware is that FD has dedicated themselves to support: the min GPU is a Nvidia GTX 470, released almost
ten years ago. That is like releasing a game in 2002 that should run on a computer that barely runs Wolfensteind 3D!