The Application Note specifically says that it is written to work with a UART connection, hence if you setup a valid UART connection between your host and cypress chip then it should be the same procedure. The HEX file itself that you upload onto the bootload cypress chip will have to be formatted the same way as the PSoC Creator IDE outputs it. Most C code is pretty easy to port to other devices, but the procedure for running it on another device will depend on the device itself. Without telling us: what "non-cypress" chip you are using, you would have to look up how to run the code for the bootloader on that host yourself.
I figured this out anyways. I had to change the UART implementation. Thank you.