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