This might be a stupid question, but do we need to download/use that installer? I ask because every other game I've downloaded from here hasn't needed to be installed just downloaded and unzipped.
No, you can use either the zips or the installer. The installer was made so you don't have to re-download the zip every update saving you ~4Gb per download (its also the only way to get uncompressed though Itch as CoR is too large [6.04 GB as of 0.65] to be stored on Itch without compression). It has auto-updates, which also means it will apply any bug fixes automatically.