Is an Ibex a deer? How is it doing that??

It's in the goat family!

The Alpine ibex (Capra ibex), also known as the steinbock or bouquetin, is a species of wild goat that lives in the mountains of the European Alps. It is a sexually dimorphic species with larger males who carry larger, curved horns. The coat colour is typically brownish grey. Alpine ibex tend to live in steep, rough terrain above the snow line. They are also social, although adult males and females segregate for most of the year, coming together only to mate. Four distinct groups exist; adult male groups, female-offsping groups, groups of young individuals, and mixed sex groups.

https://en.wikipedia.org/wiki/Alpine_ibex

I'm amazed at how casually they walk across, without even looking down!

Yeah, that casual walk of the wild goat is very impressive!