If I subscribe to Indie, I will be unable to edit my creations from within the Unreal Engine 4 editor unless I also subscribe to the Engine as well?

Yes, you can use the engine with your Houdini Indie license

If you want to run ONLY the engine in OTHER computers you can just buy the engine version.

HOUDINI ENGINE PLUG-INS
Your Houdini Indie license can be used to run Houdini Indie in batch mode or to load Houdini Digital Assets into other content creation apps such as Autodesk® Maya,® Cinema 4D , and 3DS Max® , or game editors such as Unity® and Unreal® . Houdini Digital Assets can be accessed from the Orbolt Smart 3D Asset store or created in Houdini Indie for sharing with other artists.

Ok, so one way to think about it is that the regular Indie license also includes an Engine license, but registered to the same machine?

If I want another project member to use content that I created with Indie, but on a different machine, then I need 1x Indie license (for me) and 1x Engine license (for project member). This assumes I am the only one creating content outside of the UE4 editor.

Correct?

Yup, that's correct. As varomix said, the “Houdini Indie” license is needed to create assets. The “Houdini Indie” license can also be used to run Engine plugins. And the “Houdini Engine” license can only use assets that other people have created.

So if the user only wants to use the assets, they only need the “Houdini Engine” license. Note that there's a difference between the “Houdini Engine” license and the “Houdini Engine Indie” licenses. The regular “Houdini Engine” license cannot open Indie assets. (This is so that the Indie restrictions are broken.) So in order for other people to use your Indie assets, they also have to be using a Indie licenses, which means either “Houdini Indie” license and “Houdin Engine Indie” license.

As a side note, the “Houdini Engine Indie” license can also be used to run hbatch, which is a command line tool for batch processing and scripting.