It appears that
Bryce 7 can install on a 64-bit Windows 7 OS quad-core machine, BUT - ....
It also installs an out-of-date Microsoft Visual C++ build which has to be updated.
I did not know about this after installing Bryce, so I attempted to launch the app, and I received a system error message about side-by-side application failure blah blah.
A little research through the internet pointed me in the direction of updating the Visual C++ item. To make things easy for myself, I simply ran Windows Update and voila, it pulled down exactly the item I needed and installed it. No need for me to figure out which what who how download to get from the Microsoft website.
Bryce will launch correctly now.