@sparcher, I’ve checked on my system (Gnome DE, google chrome the same version you have).
Adobe’s page in my case says:
YOUR SYSTEM INFORMATION
Your Flash Version -- 32.0.0
Your browser name -- Google Chrome
Note my version is 32, while yours reported is 24.
Please follow @alciregi’s suggestions to try to update chrome’s built-in plugin.
In my case, even after trying to update chrome’s plugin and enabling flash I’ve got the following result:
Adobe’s test page – after reloading it I see Google Chrome’s popup saying “Adobe Flash plugin is blocked because it’s outdated” with two buttons: [Update plugin] and [Run once]. Update plugin takes me to the https://support.google.com/chrome/answer/6258784
However if I click run once – flash content loads successfully.
On Hoop Game page worked the same but only after I’ve disabled all the plugins which blocked advertisement (note a blue column on your screenshot) – Ublock origin included. After it showed me adverts for some time outdated plugin popup appeared and only after that flash content was loaded.