Why a subject not in focus in the viewfinder of an analog camera is seen as two misaligned half circles, while in that of a digital camera is evenly blurred?
The analog camera you use most likely has no autofocus and thus has a split prism. These are great for manual focusing, but not so great for auto exposure (AE), as AE is done after the focusing screen.
Since AF usually works fast (and has a confirmation by LEDs), most cameras use plain focusing screens, though some professional cameras offer interchangeable screens.
Your assumption about analog vs. digital viewfinders is incorrect. Some digital cameras still use "two misaligned half circles" for focusing and some analog film cameras do not.
"two misaligned half circles" for focusing is also called "Split Prism" and was a focusing aid used in most older, Manual Focus cameras. When Auto Focus lenses were developed for film cameras, Split prism quickly went out of fashion as it was no longer needed.
Aftermarket, third party Split Prism focus screens can be fitted to almost any Digital SLR camera for photographers who wish to still use older manual focus lenses.
Some of today's Digital cameras are Manual Focus and use the split image focus method to aid in manual focus. The Leica M8 Rangefinder is an example of a Digital Manual Focus camera that relies on a split image focus aid.
A split prism finder uses 50% of the available light for each side of the split image on the focus screen. With the advent of autofocus a significant portion of the available light is redirected to the autofocus module; which results in insufficient light for a 50/50 split at the focus screen. I.e. a split screen installed in a modern AF DSLR is prone to blacking out due to insufficient light transmission.