The m4x4 instruction multiplies a vector by a 4x4 matrix. Your guess is very likely correct.
The subsequent "mov" instruction copies input texture coordinates to the output, without modifying them.
Dp4 is a dot product with 4 components. In the two last rows, the dot product of vertex position and some constants are stored in the second texture coordinate output register. That said, the meaning of the constants c4 and c5 is unknown. Taken out of the context in which the code is used, it is very difficult to guess the actual purpose of the instructions. Dot product, in general, can be thought of as a measure of similarity between two directional vectors.