What is this trapezoidal logic gate?

It's a multiplexer. When the input on the side has a specific value, the input corresponding to that value is propagated to the output. It's not a single gate per se but rather is composed of several gates that implement the function.

I's a multiplexer.

Logically it is the same as the following circuit:

^{simulate this circuit – Schematic created using CircuitLab}