How do I install this file?

Sorry guys, complete noob here, if it's not in the snap store I'm lost.

I downloaded Mari from https://www.foundry.com/products/mari/download

How do I safely install this?

Distributor ID: Ubuntu
Description:    Ubuntu 20.04.3 LTS
Release:    20.04
Codename:   focal

From the docs. You can simply run:

chmod +x Mari4.7v4-linux-x86-release-64.run
sudo ./Mari4.7v4-linux-x86-release-64.run

You will then presented with EULA which prompt you to accept it.

The official docs pretty much cover everything you need to install → https://learn.foundry.com/mari/content/getting_started_guide/installation_licensing/installation_linux.html