How to turn TSP into minimum hamiltonian path?

The dummy point allows you to have the connection between the two ends at an arbitrarily large distance. In the TSP the two ends would also have to lie very close to each other in order to minimize total distance. In your path problem this requirement does not exist and so a TSP optimum is subjective to a constraint not valid for your problem and thus may not be an optimum to your path problem.

If you introduce a dummy point (or think of it as a shortcut, a wormhole) your ends may lie far apart without affecting your distance.