Different graphics formats store things in different ways. This isn't usually a major problem with 2D graphics, but it's more serious with 3D graphics.

For STL, the documentation notes:

[STL] Stores a solid 3D object as a surface formed by a collection of adjacent triangles.

So for some reason Tetrahedron doesn't convert over to a list of triangles. It's not a very commonly used graphics primitive. There's a lot of ways we could go construct this shape, but this is what I would do:

pts = {{0, 0, 0}, {1/2, Sqrt[3]/2, 0}, {1, 0, 0}, {1/2, Sqrt[3]/4, 3/4}} 

Polygon /@ Subsets[pts, {3}]

Graphics3D[Polygon /@ Subsets[pts, {3}]]

This does export to Stl since Polygons are relatively straightforward to export to STL