Thank you, Garyk, that resolved the Chrome login troubles. That is, checking that "Always allowed to run" option for Adobe Flash Player in Chrome plugin settings, as pictured in that screenshot.
However, I'm sure you'll admit WGT can't expect their regular non-techie site users to be delving into Chrome plugin settings just to be able to log in to the site. 
If the desktop game can't get away from Flash completely like the iPad/iPhone game was able to, at least the login screen – for the sake of these forums, and so that it's possible to manage our profile pages and PMs and Wall posts and blogs – should be displayed without fail outside of Flash on each and every mobile phone and tablet (let alone every desktop browser in its default settings).
Similarly, I'm sure there are workarounds allowing you to run that pest, Flash, on an iPad or an iPhone, but it's too much to ask from regular WGT players. I just don't wish to see any trace of Flash on my iPad/iPhone, period. Steve Jobs was right.
As to testing the game itself in Chrome on a desktop/notebook, I'm not even interested. The desktop game is simply no longer relevant for me. I'm very, very happy with the 100% smooth way WGT golf is running for me on the iPad/iPhone. It's an almost perfect copy of the original desktop game, but minus all the Flash-related bugs and meter stutters! 
The only deficiences and flaws I'm aware of in the mobile WGT game currently are the 8 listed earlier in this thread (and some of them are very minor). Apart from those, WGT on mobile is perfect as it is.