What you are talking about is barycentric interpolation, which is what this is doing.
There are already image resizing algorithms that use triangulation (and something called DDE - data dependent interpolation) so the answer to your question is yes it is absolutely a valid idea.
"Phong" refers to two distinct but related things: The Phong reflection model (Ambient + Diffuse + Specular) and Phong shading (normal vector interpolation).
Correct (I over simplified). Neither really applies here because the interpolation is based on barycentric coordinates, which is the Phong part that was probably being referred to.
What you are talking about is barycentric interpolation, which is what this is doing.
There are already image resizing algorithms that use triangulation (and something called DDE - data dependent interpolation) so the answer to your question is yes it is absolutely a valid idea.