If I take a Ford Focus and call it a Mustang, is it? Arguably, no. Mustangs have a distinctive style, feel, feature set, intended audience. It's a matter of what people expect when they buy the thing.
The Mach-E kind of snuck in. I believe they intended to make more electric Mustang-branded cars, but things changed internally and priorities shifted. Lots of women really like Mustangs, and the Mach-E is positioned to appeal to many of the same people: it makes sense to use it as a kind of Trojan horse to ease folks into EVs with a brand they already like. But if you took a Mach-E and hid the name and asked folks "is this a Mustang?" The answer you'd get is "No".