In other words: sure, if someone is willing to implement a s*** tons of APIs on XP/Linux, he could potentially make it run, but realistically speaking, no one is ever going to do that.
On top of this, it's closed source which means that it cannot be modified and recompiled but its own calls have to be implemented in the kernel or a wrapper has to be used. Not only it won't run on older OS like Windows 7, but there are so many missing calls that even open source implementations of Windows APIs like Wine and ReactOS would not be sufficient to run it.
As to the other version of Edge, the old one, sure thing it had its own engine, but the whole programme was made with Windows 10 and 10 only APIs which means that it's strictly interconnected with the host operating system (Win10). The new Microsoft Edge uses the same engine that Chromium uses, hence the fact that it's not gonna run on XP.