Hah... Well, I have a personal theory about why we Americans call it "Gaelic". Given that we had ancestors come over in the 1600/1700/1800s and our ancestors wouldn't have had a good way to communicate back home (no phones, spotty letters, etc) it's possible that the change occurred in a language reform in Ireland, and that American's referred to an older colloquial usage that generally referred to both Scottish and Irish, but I'm not sure.
There was at least one Irish language reform in the past century, but by that time any Americans with heritage would have been long ingrained with whatever old useage came over to the states and we'd have had no way of knowing the "proper" name.
It's also possible that there was just a mixup regarding the name, and it just stuck and we never knew any better. Gaeilge and Gaelic are far too similar, imo. The Wikipedia page on Scottish Gaelic also mentions that "Gaelic" may refer to Irish outside of Ireland and Great Britain: https://en.m.wikipedia.org/wiki/Scottish_Gaelic
I've met 0 Americans that knew it should be called "Irish" and 100% of the Americans I've met who even know that Ireland has a language that isn't English think that it's called "Gaelic" unless they are actively learning the language. In fact, it's common for people to say "You mean Gaelic?".
The vast majority of people think I'm trying to cultivate an Irish-English accent when I tell them I'm learning Irish. ;)