I suspect it's all because of our corporate proxy. I'll try from home later.
It opened thank-you.html and hung there.
For some time I had difficulties in reproducing the issue as reverse proxy started opening our corporate proxy url and fails.
The problem is that the address in reverse proxy url is not the proxy I set up in WinInet settings (Windows10):
But in WinINET:
It looks like that all browsers when they are run by the tool ignore system proxy settings.. (my guess).
If I disable proxy at all (so I couldn't open any site in browsers) running TestCafe still works: it opens the first page ("http://devexpress.github.io/testcafe/example/") and hangs on thank-you.html.
It was in running state (only fixture's name was output)