Do Computer keyboards have ICs?
Even the earliest mainframe computer keyboards had circuity! Keyboards buttons are usually placed in an X-Y matrix such that any inputs need to be converted to some serial code (scancodes or keycodes) and sent to the computer. The matrix reduces the number of individual buttons to scan which in a keyboard, saves a lot on wiring and processing power. The scanning procedure typically involves iterating through every combination of rows and columns to check if button press:



The use of the matrix created several well known problems such as rollover. When multiple keys are held down simultaneously, this circuit is unable to register all the inputs. Modifications in the both the layout of the keys and software of the microelectronic later improved these conditions. 

Also, if you might have heard of the connection types PS/2 or USB (and of course the AT Connector) which send serial communication through these ports. These standards regulate the communication protocol between the keyboard the computer, necessitating the microcontroller.

Image Source:
https://en.wikipedia.org/wiki/Computer_keyboard#/media/File:FunctionalCircuitDiagramOfKeyboardNumPadScanningProcedure-small.gif