I can see what you're arguing, but I think this is so abstract as to not really be meaningful. At no point is there a tree data structure. I suppose there is one if you extend it into the fourth dimension :)
> And I'm curious what makes you say that an assembler doesn't count but source to source compilers do.
I think for me it's because an assembler doesn't have any choice about how to translate the program. A compiler has more freedom for how to translate the program.
I'd then say a transpiler is a form of compiler, but an assembler is not.
> And finally, yeah I've seen references going back to the sixties, but they're almost always marketing literature.
See for example The Communication of Algorithms by A F Parker-Rhodes, 1964. This is a peer-reviewed academic paper, not marketing material.