Quoting from the Kodi documentation you referenced as 'read':
Select LibreELEC or OSMC and press the Install button.
You'll be prompted to confirm. This will delete any data on the SD card, so if you previously had Raspbian on it be sure to back up your files first.
These sentences answer two of your questions:
- Must OSMC be installed and why exactly is it needed?
A: No - you can install either OSMC or LibreELEC. They are Operating Systems, and you must have one of them to play the media you want.
- Is it correct that OSMC is an operating system and therefore would replace Raspbian?
A: The documentation says it's an OS - and it is an OS. And yes, it will replace Raspbian - following the instructions will overwrite whatever is on the SD card.
- If this is correct should I simply follow the backup steps to save the current state of my Pi?
Yes, the SE question you've referenced may be used to create a backup image file that you can later restore to your SD card if you tire of Kodi, and wish to resume using Raspbian. I would only add that for the cost of a small SD card, you can have both OS's, and simply swap SD cards depending on what you wish to do at that time.