Google Chrome has stopped supporting NPAPI which is the technology the game launcher plugin relies on to start the game.
If you want to be able to launch the game while using this browser you can re-enable NPAPI support with the following steps:
You can read more about this here.
Go to the following URL: chrome://flags/#enable-npapi
Choose 'Enable' under the 'Enable NPAPI' heading.
You should now be able to start the game.