No they never forced them but they said "hey here's this really awesome sandboxed platform that runs on almost any os, and it's a modern browser!" That's really enticing to a platform like steam where most of their app is web based. Steam isn't a desktop application, it's a hybrid application that needs a web browser. Do you know how hard it is to upkeep a modern browser? There's a reason it's pretty much only chromium and Mozilla making browsers. It's not laziness, it made sense, and Google was the only one making anything like that at the time for developers to use.

Once Google had the market share, they started making changes that they knew would affect everyone using their platform, and that's how they wanted it.