I need fonts that are commonly available on desktop platforms (Windows/Mac, base system + MS Office) that are similar to Gotham Narrow and Google Yrsa.
I've seen mention that Arial is similar looking to Gotham but I don't know.
Although Arial is similar to Gotham Narrow, it has attributes which are very dissimilar, notably the tails of lower-case letters like a, e, g, s. Capital letters are probably a little too wide, too. A better alternative might be Segoe UI, which is probably available on recent Windows systems.
Here's Gotham Narrow, Arial Nova and Segoe UI. Unfortunately it wasn't possible to make everything exactly the same size, but it's possible to see that Segoe UI is very similar in shape to Gotham Narrow.
Roboto from Google Fonts is free and pretty close to Gotham Narrow. Certainly not in the same league as Gotham is a top-end commercial font, but give it a try.
Please note, using non-system fonts means whoever gets your document also needs to have the fonts installed.