I’m not denying that Mozilla has a history of poor governance. But they are the competitor to Google here. You need to consider these things in context to understand what anti-corporate means for the internet.
It absolutely matters. We need to consider that a right-wing actor is likely to exaggerate claims against an organization that is ostensibly socially-minded and represents anti-corporate interests, like Mozilla.
Fallout 4 came out in 2015. They had plenty of time to start work on a new engine since then.