A “Mechanics First” or “Systems First” approach to game design. As a method it is concerned with Atomizing and Abstracting Game Mechanics down to their fundamental Game Design Patterns and assembling them into novel rules constructs before considering what narrative or theme the system is attempting to communicate.
Because games are made of smaller games all the way down, a common creative mashup technique in Bottom Up design is to identify pattern-metaphor relationships that resonate with your new mechanic in other games and swapping them out.
The opposite of Top Down Game Design
Practical Creativity by Raph Koster, GDC 2014 Game Design Koster’s Taxonomy of Games