No, the software doesn't run on Windows 10 operating system due to compatibility issues. Besides that, PhotoArtmaster Gold was never released to support Windows 10 and modern operating systems.
If you want a replacement for this application, then I recommend checking the PrintMaster v7 Platinum. It might not be the same application as the PhotoArtMaster, but it successfully meets the common image manipulation and printing.
You can access the homepage of the application through the following link: http://www.broderbund.com/p-860-printmaster-v7-platinum.aspx