I followed your link and downloaded it as a .ttf, which I then moved to ~/.fonts
I do agree with you that I am confused as to your intent. The UI on your screen composes the UI of the applications.
The interface is essentially Your Window into the operation of the computer.
The tip I gave above in regards to using a custom .css may give you the fine-point control over the UI of most apps... I can probably help you I.D. the classes you need to specify if you clearly define what Interface elements you wish to change. But the Browsers would be another story. They will (should) use the system Font... but to customize the individual elements within the interface, you would need to get into the webkit .css.
Some browsers, like Vivaldi, make this quite easy. Most do not. They are like Gnome... Their Browser Appearance is their recognizable Brand Image and they lock you out of customizing that.
With a lot of hassle, you can extract the .pak files and change the contents, then recompile... Only for the Next Update to undo all of your work.