Yup, that guide mentions getting to a later version of Android requires jumping to a custom ROM. That explains the need of CWM, but as I mentioned before any custom recovery will do. I prefer TWRP these days but with older devices I found CWM to be better. The stock recovery will not work as it only accepts files from Motorola and not any custom ones.
Reading the guide, this is the steps I would take:
1) Install ROM manager and then install CWM (or any other custom recovery if it offers a choice, wouldn't really make a difference).
2) Copy the complete ROM zip file to the base of the storage, so it's not in any folders.
3) Restart the phone into recovery mode via ROM manager. Then back up the phone.
4) Wipe the following partitions: system, data, cache and dalvik cache. Do not wipe any other partitions like internal or SD card, otherwise you will delete the ROM you copied over.
5) Now choose the flash option and select the ROM file. This will flash everything. This will take a good 10 minutes or so to complete. Once it finishes it will either auto reboot or asks to reboot (depends on the custom recovery). Reboot the phone and it will load up the custom ROM.
You will not need to flash anything else. Firmware usually contains files like basebands and stuff for the modem, wifi, bluetooth, etc to work but you should not need to do that.