Dark matter/energy does exactly that, un-observable theoretical concepts to explain contradictions between reality and physical laws
You got that backwards. Dark matter and energy are things we observe that can't be explained by existing theory. That's why they're "dark": no accepted explanation for them.
Why can't dark energy explain emDrive then?
Dark energy has been quantified, and it's really weak. Vastly weaker than gravity, and that's saying something. It's only the dominant energy in the universe because it's present in empty space - even the very empty space between galactic clusters - which makes up most of the universe by volume.