I presume the next logical step is what YouTube have done and use HTML 5 as a player as that'll work in any (modern) browser but I suppose it'll be a logistical nightmare to port it over.
The real challenge is support for the DRM protection in browsers, there's no single standard so different browsers/devices require streams encrypted with different DRM software. The PlayReady DRM currently used by Sky Go is only supported by Edge/Internet Explorer.
Netflix and Amazon get around this encrypting their streams in a number of DRM schemes which cover most browsers/devices, which is trivial for them as all their content is on demand. Sky Go has live streams which significantly complicate it.
Firefox recently added support for the Widevine DRM that Chrome/Android use, which simplifies things a bit, but Edge, Safari, iOS and games consoles still require other DRM schemes. To hit most devices, you basically need to encrypt all the streams in Widevine, PlayReady and Apple's FairPlay.
I imagine this is the main reason Sky have stuck with Silverlight for so long, as until fairly recently support has been hit and miss (and is still problematic). Amazon and Netflix were Chrome only for their HTML players until not long ago. The appearance of streaming via the download player on Mac's would suggest that this is the problem for Sky, as using an Electron app allows them to migrate to Widevine and stick with just that without having to worry about different DRM for different browsers.