Can you put the 3D Unity game on the Xamarin cross platform?
It depends.
Assuming you're not talking about games in a browser, Unity creates its own executable and / or entry point. You will probably have to accept the game created by Unity3D and embed it as a resource in the original application, say, the Windows Phone application. Then run the game as a child process.
Original app:
You may be able to embed the Unity3D application for Windows created as a resource in an existing Windows Phone application. Could you just create it as a child process?
Web game
However, there is nothing to prevent you from making a game in Unity3D and creating it to create a web game.
Access to additional build functions for publishing on the Internet in Unity 5. After the user installs it, the extremely popular Unity Web Player plugin is updated automatically. Use it to deploy to Internet Explorer, Safari, Mozilla Firefox, etc. Tell us more
In your Xamaring application, you can simply display a web browser from which you can play your game.
Shell Browser Applications
I see that your Merricks Jewelry app is already in the iOS store. Be warned that if you stick to the web game approach, I know that at some point Apple strictly adhered to its own applications, which were essentially shells for web content. You may need to contact Apple. It may or may not be.