I can`t use Royal TSX to manage vCenter and ESX today via html5 interface. Safari webplugin is not supported by VMware because lack of full html5 compatibility. For example, tasks are not displayed, blue screen instead of login prompt in esxi.
we don't currently have a Chrome plugin for Royal TSX and there are no plans to change that in the near future.
Unfortunately there's no Chrome framework on macOS that we could use to integrate Chrome into Royal TSX without major effort and a huge increase in download size and performance impact for the whole app.
While it's really unfortunate that the VMware web client currently does not work properly with Safari, that's something VMware has to fix on their end.