I just checked and American Typewriter ITC Pro is available in Adobe Fonts, but that doesn't mean you have the Adobe Font ITC Pro version on your Mac — it could be another version.
When you filter your typefaces on your Mac, can you tell if it's the Adobe Font Version?
When you go to Adobe Fonts from the Creative Cloud app, does it say American Typewriter is activated?
Assuming you have a paid subscription to Creative Cloud and are logged in with the same Adobe ID on both computers, it should show in both. If it doesn't, try logging out and then log back in again and restart your computer. If you sign out of Creative Cloud, then your Adobe Fonts will not show up.
There are a couple of things that could be going on here, so please let us know if this works or if you need more assistance.