A triangle is the simplest primitive that can be described in isolation because it has three points, fewer than which do not describe a surface in 3D.
Because a triangle can be considered in isolation, it is possible to make a piece of code or silicon that is capable of rendering only a single triangle, which via the power of repetition can render any surface at all.
Therefore, the first computer system which succeeded at rendering "any surface at all" naturally did so by rendering many triangles independently.
If one thinks of triangles and quads as "primitives" (i.e. as completely isolated bits of geometry with no context) the triangle is the more primitive, and so it will tend to "win."
However, once entertainment-grade computers exceeded a certain level of sophistication in the 1980s, the simplicity of considering "primitives" in isolation became less important. If graphics are to be mass-produced, then economies of scale favor processing groups of related vertices, much as they favor assembling a hundred near-identical cars at once.
This is why in the 1980s, movies adopted the "quad," which is a misnomer because it refers to a 2D grid of vertices in 3D space, and not an isolated quadrilateral.
The same shift from triangles to "quads" has not happened yet in the realm of interactive entertainment, but it is likely to happen, fairly soon, and for the same reasons it happened in the movie business.