What Allen did was write an 8080 emulator that ran on the -10. The 8080 is a simple CPU, so writing an emulator for it isn't hard.

https://pastraiser.com/cpu/i8080/i8080_opcodes.html

Then, their BASIC was debugged by running it on the emulator.

The genius was not the difficulty of doing that, it wasn't hard. The genius was the idea of writing an 8080 emulator. Wozniak, in comparison, wrote Apple code all by hand in assembler and then hand-assembled it to binary, a very tedious and error-prone method.

In the same time period, I worked at Aph, and we were developing code that ran on the 6800 and other microprocessors. We used full-fledged macro assemblers running on the PDP-11 to assemble the code into binary, and then download binary into an EPROM which was then inserted into the computer and run. Having a professional macro assembler and text editors on the -11 was an enormous productivity boost, with far fewer errors. (Dan O'Dowd wrote those assemblers.)

(I'm doing something similar with my efforts to write an AArch64 code generator. First I wrote a disassembler for it, testing it by generating AArch64 code via gcc, disassembling that with objdump and then comparing the results with my disassmbler. This helps enormously in verifying that the correct binary is being generated. Since there are thousands of instructions in the AArch64, this is a much scaled up version of the 8080.)

The Wozniak method was how I used to write 6502 assembler programs in high school since I didn’t have the money to buy a proper assembler. I wrote everything out longhand on graph paper in three columns. Addresses on the left, a space for the code in the middle and the assembler opcodes on the right, then I’d go through and fill in all the hex codes for what I’d written. When you work like that, it really focuses the mind because there’s not much margin for error and making a big change in logic requires a lot of manual effort.