I do get Minecraft to work in windows 10 with the windows 7/8 installer.
However I am under the assumption that the windows 7/8 installer is supposed to work with both windows 7 and windows 8. - Well, I can't test the installer on windows 8 because I do not have a copy of windows 8, but I do know that Minecraft fails an authentication attempt on windows 7 with an 401 code.
Here is the important part of the log file:
<Log file start>
19:45:32.920 Environment: authHost='https://authserver.mojang.com', accountsHost='https://api.mojang.com', sessionHost='https://sessionserver.mojang.com', servicesHost='https://api.minecraftservices.com', name='PROD' 19:45:33.730 Failed to verify authentication com.mojang.authlib.exceptions.InvalidCredentialsException: Status: 401 at com.mojang.authlib.exceptions.MinecraftClientHttpException.toAuthenticationException(MinecraftClientHttpException.java:56) at com.mojang.authlib.yggdrasil.YggdrasilUserApiService.fetchProperties(YggdrasilUserApiService.java:132) at com.mojang.authlib.yggdrasil.YggdrasilUserApiService.<init>(YggdrasilUserApiService.java:44) at com.mojang.authlib.yggdrasil.YggdrasilAuthenticationService.createUserApiService(YggdrasilAuthenticationService.java:153) at dxo.a(SourceFile:670) at dxo.<init>(SourceFile:424) at net.minecraft.client.main.Main.main(SourceFile:199) Caused by: MinecraftClientHttpException[type=HTTP_ERROR, status=401, response=null] at com.mojang.authlib.minecraft.client.MinecraftClient.readInputStream(MinecraftClient.java:78) at com.mojang.authlib.minecraft.client.MinecraftClient.get(MinecraftClient.java:48) at com.mojang.authlib.yggdrasil.YggdrasilUserApiService.fetchProperties(YggdrasilUserApiService.java:113) ... 5 more
<Logfile end>