You can call that emulation in both cases. At least, I do. That answers Bruce's post as well.
In both cases, the 8080 instruction set is emulated. The fact that it merely requires a translation is what made it easy and simple, but that's still "emulating" a 8080.
And no, I wouldn't call the assembler you mentioned a cross-assembler, at least not in the usual sense. A cross assembler typically takes assembly code for one CPU, is run on another type of CPU (thus the "cross" term), and translates said assembly code to machine code for the CPU meant for the assembly code in question. The one assembler mentioned here would *translate* 8080 code to 8086 machine code that would execute as intended. That's emulation in my book, not a cross assembler. Again a simple form a emulation only requiring translation - and, in the assembler case, the translation being done *before* running, while in the hardware emulation mode, it was done in real-time.
Now if you want to nitpick about what "emulation" is or is not, have at it.