That's usually called "mirror writing", but it's a different concept. If you look closely at these examples, you'll see that the letter forms are carefully chosen so that the texts are still readable as normal under symmetry (unlike regular text).
This is done by creating letter forms that can be interpreted as other letter forms under symmetry, similar to the u and n being interpreted as each other's inverted forms. These ambigrammists are making designs in which more pairs of letters have that kind of relationship.
Yep, I've always had a really easy time making ambigrams because of my (natural) mirror writing ability. As in, one day I tried mirror writing and I could just... do it without hesitation.
I have asked a few left handed and right handed friends of mine to make ambigrams, or do mirror writing, and it's quite interesting how easy it is for left handed people compared to right handed people.
Oh sorry, I thought you were conflating the two because the talent you described was for mirror writing.
I'm also left-handed and learned belatedly that I can do mirror-writing with my non-dominant right hand. I'm not that coordinated with that hand, so the writing is a bit messy, but it doesn't seem to require noticeable extra cognitive effort to do the mirroring.
I could also pretty easily read upside down or backwards from around the time I learned to read.
However, I've never found it easy to make ambigrams!