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.

No, the Xbox 360 SmartGlass app is not compatible with Windows 10. However, Microsoft has a newer app called Xbox app that works on Windows 10 and provides similar features such as remote control, streaming, and social features for Xbox One consoles.

All Smartglass apps have long since been discontinued. Short version is They were around for a very short period of time, and no one used them, so developers stopped making the apps for it, and the feature is no longer supported in any Xbox platform