It's Firefoxs fault that Chromium took over, Firefox just had to copy what Google did with Chrome (which is make a version that is easily integrated in other applications). It had years to do so, and did not. I am not blaming Firefox for the rise in Chrome, but I am blaming them for the rise in Chromium. They have a solid alternative and didn't care enough to capitalize on it. Who knows in another timeline with changes it's possible Firefox Gecko rained supreme in the embeddable space.
So let's say you're a bunch of ex-Opera employees who want to start a new browser, are you going to write an entire browser engine yourself? No who has time and money to pay hundreds of developers for years just to catch up. You're going to use a off the shelf version and modify it.
Can you use Firefox? No, good luck integrating it into anything, it's extremely difficult. Firefox actively suggests not trying to embed it.
Can you use Chrome/Chromium? Yes it's easy and readily available SDK that even has thousands of implementation examples.
Can you use Webkit? Yes you can, but it's only managed by Apple and a select group of smaller companies, you are at the mercy of Apple. It also has poor support in some areas.
So you end up going through pros and cons and Chromium is the result. It's not the result of a bunch of Google loving companies, it's just pure developer economics. It gives you the best possible start.