Gitlab and Element's website structure is different. element.io is the site for the managed product, so even their "on-premise" installer is meant to be used in a commercial relationship. For install docs you'd probably have to purchase their product (which isn't available freely).
You probably want to read the open-source software's installation instructions at: https://github.com/vector-im/element-web
TLDR, check out the project, run `yarn install`, then edit the config file, then `yarn build`.
And, yes, that is all there is to it. It's significantly simpler to deploy than GitLab.
Finally, you keep mentioning self-hosting; you _can_ just use a non-self hosted application like the downloadable version of Element, SchildiChat, Fluffychat, or any other client.
No reason to bring hosting into the mix for the client, if that's causing concern.
You probably want to read the open-source software's installation instructions at: https://github.com/vector-im/element-web
TLDR, check out the project, run `yarn install`, then edit the config file, then `yarn build`.
And, yes, that is all there is to it. It's significantly simpler to deploy than GitLab.
Finally, you keep mentioning self-hosting; you _can_ just use a non-self hosted application like the downloadable version of Element, SchildiChat, Fluffychat, or any other client.
No reason to bring hosting into the mix for the client, if that's causing concern.