I had this happen to me recently. I was unable to play Destiny at all, it just wouldn't start, get stuck on the placeholder image screen, and then the popup would show.
I'm not entirely sure what caused it to start working again, but I did try and open another game then go back and try Destiny and it worked.
I was running into the same problem ("Reopen game") pop-up after connecting effort appeared to time out.
Google Support had me try some things, but none of them helped. But I have finally figured out what was the cause of the problem for me. Your mileage may vary.
For me, it was a Google Chrome extension for "Private Internet Access", my VPN service of choice.
Once I went into "chrome://extensions" and flipped the slider to disable the extension, then closed all browser windows, and opened a new one, Stadia worked. I could get into a game and play.
Please note. You do not need to remove the extension (if you have this one), but you need to disable it.
Also, it doesn't matter if you are actively using the PIA VPN. As long as the PIA extension icon shows up at the top of your Chrome browser, Stadia is not going to work.
I have not tried other VPN services, but if you use ANY VPN, you may want to try disabling if you have a similar connection issue.
I have reported this to Google's Stadia support team.
I'm also having this issue.
Windows 10 Pro
Chrome (other browsers are blocked anyway)
I've tried adding the google domains to chromes whitelist for pop-ups - didn't work
I am certain it's a network issue. I have a VPN. If I use the VPN the game will open but the performance is slow and unplayable. If I don't use it, the game will open approximately 3% of the time and then works perfectly. Having to re-try continuously is absolutely infuriating.
I suspect it's a range of IP's and/or ports that are blocked at the ISP level... Probably something to do with some poorly configured spam filters they use to speed up the internet.
So I've been trying to play anything via Stadia, but get the reopen the game to play error every single time I try it. I've disabled ad blockers, even extensions that might interfere I've disabled. I've tried it in incognito mode. Tried it in the Chrome app (even tho it's not really an app mind you), and I've now tried it on Chrome and Chromium just in case. I've set my DNS to Google, flushed DNS, and now I can't think of anything else to try.