You can absolutely run pvc straight to the return intake or output but as JDA123 mentioned you should incorporate unions at both ends to make swapping or servicing the pump easy.
I do think in some cases a flexible hose coming directly from the pump can reduce vibration noise in some cases and sometimes it is more appropriate if you need a subtle s curve in the pipe that cannot be accomplished with standard 45deg elbows.
The technical description of "closed loop" actually has nothing to do with the overflow. Its simply a means of supplying flow which is isolated to the display by plumbing both the intake and output of a pump directly from the display. In other words it acts like a power head inside the display but the pump is just external to the tank. So you pull water directly from the display and return it right back to the display. In this case the sump completely bypassed.
Here is a simple illustration that show the difference.