Elementum has a self-hosted virtual Kodi repository.
What it means?
When installed, Elementum adds a repository to Kodi. In some cases it is added, but not enabled, so you can manually enable it like any other addon.
Repository update address points to the Elementum addon, so it you Elementum cannot start - repository is not working.
This was made in that way to be able to change repository source in the code, in case github in inaccessible, or something.
Plugin knows which OS architecture it needs, so it’s downloading only that architecture zip file.
Repository contains the Addon itself, Burst addon, Context addon, you can install or update any of them.
Please, don’t use third-party repositories to install or update the addon, unless you know they are providing you with the universal package, which contains all the architectures.
So, if you addon works fine - you can simply update the addon as usually, or leave it to Kodi.
If not, then you should re-download addon from Downloads and re-install from zip. No need to remove the addon before installing.