This really is a typewriter! It is one of the simplest index typewriters -- that is, writing machines on which the action of selecting a letter is separate from the action of printing that letter.
Both the type and the so-called "keys" of the Simplex are made of rubber. In order to type, one simply revolves the wheel until the right letter is at the printing point, and presses down. As one does so, a simple device pushes the carriage or typehead forward one space.
Originally, the Simplex was meant to serve as a serious writing machine for those of modest means (the price of the first Simplex was $2.50; a Remington went for $100).