I don't know about the executable version of the game, but even though I usually don't really like the web versions of adult games because private mode prevents you from saving, this one is an exception (as it is the most up to date version)
No clue as to how I'm supposed to run it once I download it, however, when I use the Itch.io launcher, starting the game opens a new window, as if it was its own app. (Basically the itch app is its own browser, so if you prefer to separate your clean browsing history from your private one, I'd suggest downloading the Itch app)