Back on Topic
As for weather or not windows 10 will improve PC gaming I dunno. On the one hand we have DirectX12 but on the other we have the introduction of Android and iOS apps being quickly ported to windows (They demod Candy Crush at Build) and they have said that they are planning on reimplementing all of Apples APIs in Windows. This is good news for iOS and Android developers but, bad news for PC gamers who expect a certain amount of quality from their gaming stores which may now end up being flooded with low quality iOS ports.
*looks over to Steam*
I'm... pretty sure that happened when Steam let people throw anything they want onto the service.
If anything, with MS letting people put Win32 apps on the Windows Store there might be more pressure on Steam to improve. If GabeN was scared of the Win8 store which didn't even support any of the games on Steam's platform he should be running for the hills with Windows 10.
As to adoption - I think making Win10 free will help, but you'll still have people that will insist a particular version of Windows is best, despite hard evidence to the contrary. Plus you'll always have those one or two badly-coded pieces of software or games that simply won't work on the latest and greatest.
So I think the pickup of 10 will be faster then 8, but I don't think people will be making 10-only games for a while. It's more likely they'll port their XB1/PS4 renderers to DX12 and have it as a choice between 11 and 12 instead.