After some more research on my side, I was able to find a solution.
In CSS, you can use the @import function to import a font from Google Fonts (I do not know if this will work on fonts not already made available by itch.io)
Below is the code snippit I used for my page theme:
@import url('https://fonts.googleapis.com/css?family=Ultra');
This was used in conjunction with the previously shown "font-family" CSS code to set the font.
It is important to note that I had to place this code at the top of my CSS custom code.
The site used for reference was a w3docs page.