What is the browser engine on Android devices? Different vendors send non-Chrome browsers by default. Can I assume all of them to be Chromimum based?
No. 

The default browser on stock Android is Google Chrome. This uses the Blink layout engine. For AOSP installations without the Google Apps, the default browser is the old "Browser" app that uses Webkit.

However, other browsers are available. Firefox uses Gecko, Opera uses Blink, Dolphin uses Webkit, and there are probably others. Additionally, I am informed in the comments that Samsung and HTC install different (non-Chrome) browsers on their phones. I do not know what they are, or what engine they use.

Summary: Android does not have a single browser or layout engine.