Can anyone tell me if this game works on Windows 7 64bit please?

Yes.
GOG have listed all the Links games to be compatible with Win 7.

Well what GoG says and what reality is are often far, far different things; I have had probably 20 of their games so far that either don't work at all; freeze on menus, or have bad serial keys across 6 different PCs regardless of Windows XP/7/or 10 being used. So I'm just looking to see if this is another broken game or if it actually works properly on windows 7. Because if it's something like ArmA 1 with a bad serial key or Hidden and Dangerous 2 with a mouse that won't move; then I'm better off going to ebay and getting it on disk and using my Windows 98SE pc.

Couldn't tell you if it will work for certain on Win 7. I couldn't even tell you how well it works on Win 10. I play all my old games on old operating systems.

If you have this same option, why not just buy the pinnacle of the Links LS series, Links LS 2000 and run it on your 98SE PC?
An old system is the best option for old games. I'm running all the Links LS series with the exception of Links 97. I may even get this one working just for the sake of it.

I can confirm that I am able to get through multiple courses, consistently, without crashing, plus view all the walkthroughs and videos etc. I have all the animated options, skies, etc, turned on.

...All it took was attempting literally every single Compatibility Mode setting, until I found one that didn't randomly crash out of the game. Windows NT 4.0 (Service Pack 5). Why? Who knows. I'm amazed it works at all.

I was pretty close to requesting a refund before though.