There is a still huge industry of web games (99% of them in Flash) because that is still the best technology to write cross-platform games in the browser. Kongregate, Armor Games, millions of people playing games on Facebook.
I wouldn't exactly call it a huge industry, it's been shrinking for years as indie devs shifted focus to mobile and steam. FGL.com the main marketplace for monetizing flash games has scheduled shutdowns [1] of all their flash services to focus on their mobile services, they also announced their ad revenue as one of very few providers was collectively down to $50/day [2] when they announced that was shutting down last month.
Flash games are easily a multi-Billion dollar a year industry. You mention games shifting towards Steam. I'm pretty sure that there are a lot of games on Steam that are still created in Flash. Flash (through Air sdk) provides an amazing way to target web and all major mobile platforms with the same code base.
Also, I wouldn't judge popularity by money made through ads. The industry has long since shifted to in app purchases.
Can you show any Flash games making heaps of money? I have games of my own on both Kongregate and Armor Games from late last decade / early this decade, the business models behind that type of flash game (which was mostly licensing and ads) has almost entire disappeared and not been replaced.
Edit: Also, I believe Kongregate has a whole ton of games with In-App Purchases. I don't have any experience publishing on there but I do have experience on Facebook.
While it has declined, it is still almost a billion dollar industry on its own just on Facebook. You asked for "examples of games making heaps of money" and I included links to a bunch of them.
Just to clarify, when you say "shutdowns of all their flash services" this means they shut down their distribution system that was for distributing your game to portals automatically as well as one other service. They didn't shut down the flash game marketplace or stop all flash-related activities.
Ads (FGL Ads, announced shutdown in a separate post 1 or 2 weeks ago, follows the shutdown ~a year ago of the former largest ad company in this space Mochimedia), in-game services (Gamersafe leaderboards, achievements etc), and distribution (Flash Game Distribution). The marketplace is the only thing staying up although it's massively declined too and now has 0 people working on it after layoffs a few weeks ago.
You're right in illustrating how things are winding down - I just wanted to point out it wasn't a complete shutdown of all things Flash. Ads were never as big a component of the flash game industry they are in mobile apps: sponsorship and mtx were the kings.
