In my humble opinion, the description of "mini-computer" missed the boat entirely.  In the technological progression of the time (late 1950s - early 60s) transistors were in general use.  By the beginning of the 60s logic design had entered the "discrete component" phase.  Vacuum tubes had been replaced by transistors, but there were much greater advantages to be gained than simple substitution of transistors for tubes.  Besides the tremendous difference in reliability over tubes there was an enormous savings in production costs;  a transistor had 3 solder able leads, a vacuum tube base many more - 5 to 9 were pretty common.  But it was quickly recognized that the circuit design goal was not to deal with components, but functions.  So a whole new industry developed to supply "logic/function cards" populated with logical "gates, invertors, and amplifiers" to the manufacturers of computers and control devices (who generally held patents on the foundation designs).  Companies like TI, DEC, SDS became leaders in producing a wide range of standardized logic cards.  A lot (most?) digital design of the era was done writing Boolean equations representing the input and output signals, then searching the suppliers handbooks for the best solution translated into the appropriate collection of logic cards.  After a few development iterations of the logic cards someone recognized that a computer could be designed around the existing logic card offerings.  The architecture was different than mainframes (which were mostly based on the Erkert/Mauchly patents) and focused on a bus system of control and data flow within the computer.  This distinction apparently opened the doors for marketing them without conflict with the patents that restricted "mainframe" competition.  Eventually the function of the 'logic cards" was swept into the design of integrated circuits and the rest is history: enter the PC.