No, a low-level programming language is not defined by being closer to the metal. And high-level programming is not defined for being closer to English. Heck, BASIC was probably the closest to English, and you’d be hard pressed to defend that it’s higher-level than Haskell. Which is probably as difficult to understand for a native English speaker as any real programming language can get, with the sole exception of APL.
Anyway, indeed, some of those things are true. But they are only secondary attributes. They are like the fact that vi allows you to do much more in less keystrokes than any other editor: the core reason is that vi was designed to work over 300 baud phone lines, and this involved, among many other things, reducing keystrokes – but this was not the goal, but a side-effect.