You can add it in Google Calendar using "add URL" and it will show up in the GC app. Downside is that you need to use the app... and also it refreshes the link when it wants (you can't set it).
You can use a calendar app that can import .ics links directly. The one I use is called Calengoo. This way you'll be able to control when to refresh it, but it bypasses the normal Android calendars so it won't be visible to other apps or widgets except the one that imported it.
I noticed what you said about not using Google services. The Calengoo app has a version you can download on their website (as opposed to Google Play) and purchase a license code with CC or PayPal, that is not tied to Google Play.