Does the Xbox 360 SmartGlass app still work on Windows 10?

Smartglass is more a legacy app and still exists for those on Windows Phone 8 or Windows 8 where the Xbox App does not (yet) exist. For Windows 10, you are right in that the Xbox App essentially replaces Smartglass.

On May 18, 2018, the Xbox 360 SmartGlass apps for iOS, Android, Windows Phone 7, Windows Phone 8, Windows 10 Mobile, Windows 8, and Windows 10 will be retired. Support
for the app and content are no longer being offered.

https://support.xbox.com/en-US/xbox-360/apps/smartglass-info

Xbox 360 SmartGlass app retirement. On May 18, 2018, the Xbox 360 SmartGlass apps
for iOS, Android, Windows Phone 7, Windows Phone 8, Windows 10 Mobile, Windows 8, and Windows 10 will be retired. Support for the app and content are no longer being
offered

It's for the Xbox One Smartglass app, not 360. Also as I said, I have the issue with the Mixer app as well.

Xbox 360 SmartGlass app retirement. On May 18, 2018, the Xbox 360 SmartGlass apps
for iOS, Android, Windows Phone 7, Windows Phone 8, Windows 10 Mobile, Windows 8, and Windows 10 will be retired. Support for the app and content are no longer being
offered

No as it ss discontinued

A lot of xbox 360 apps wont workt as the protocols are defunct

Xbox 360 is no longer supported

And the xbox app doesn't support it

So using an ancient app won't help on Windows since the app was discontinued