Then you'd load a BASICODE translator program, and play that recording via the regular tape input of whatever machine was used. After which the translator program would translate the BASICODE program into something running on your machine.
None of this involved add-on hardware. Which was kind of the point of BASICODE: take machine type X, write translator program, load & run BASICODE programs. Nice concept, but too limited in practice to be of much use.
The hw mod discussed above is clearly some custom mod to use a ZX81 for a task it did not have a suitable hardware interface for (or at least not in the opinion of whoever built the mod
).