How to embed some Power BI Tiles in a Rails App?

I can feel you pain, I got very confused reading the documentation when trying to setup Embeding.

Not fully the fault of the documentation, it's more to do with the different functionality being released at different times so older documentation speaks to functionality that embed is better for now.

For your requirements of having a rails app that the user logs in and views reports then Embedded is the recommended way with the exception if it is internal (users trusted) then Azure can be used.

The Azure application method being for internal users as the token is exposed (if they go looking for it)..

The embed method needs a server iin the middle that generates short term tokens to the user.

The "server in the middle" part I go stuck at for week :( . 

The JS example you referenced if you clone it and review or look at source you can see it calls a server than returns the requried data. So for your rails app you need to build/create a server that handles that task...

Hope that helps - I'm not fully there yet either so don't take this as definitive!