Should a Knight be able to move from A2 to D3?

Nevermind.

hmm

No, because rules.

The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal.

https://www.fide.com/fide/handbook

You are at 1770 and cannot answer your own question???

Agree with some of the above, "Hmm" indeed.

They exist as threeleapers like almost everything already exists in fairy chess: https://en.wikipedia.org/wiki/Fairy_chess_piece#Leapers 

You are right it is not a threeleaper but the real threeleaper does not jump from a2 to e4, only from a2 to d2 or from a2 to a5. To jump from a2 to d3, you need the more powerful camel.

The definitions only look at the horizontal and vertical coordinates, not at the "virtual" route you have drawn in your picture.

Basically every route is virtual because knights "jump". But in terms of the definitions for all types of leapers you only travel along the lines of the cartesian grid. One system is not better than another but this happens to be the way it is done for the fairy pieces. See the table on Wikipedia.

By the way, Go-players simply call the a2-d3 distance between stones a "large knight jump".

Stones are motionless in Go but they work together in forming "nets" of stones to separate enemy groups from one another. The large knight shape is pretty effective in preventing enemy groups from "sneaking through" and "connecting".

Note: A Go-move consists of adding a stone on the board which may be used (amongst others) to create, strengthen or break through a net of stones.

I don't know if 3D Go exists and whether or not it would be playable. Changing dimensions would probably require rule changes as well. I never played 3D chess either. I don't believe it's my cup of tea and it would require extensive 3D visualization training. In the future 3D games will be played with the help of VR goggles such that you can beam yourself to any viewpoint you would like to assume and observe the piece positions around you.

"hhhhhhhhhhhhhhhhhhhhhhhhhhmmmmmmmmmmmmmmmmmmm"

Please stop. I`m getting a headache.