The big advantage would be that we're not limited to the exhaust velocity of combustion (which is inherent to using your reaction mass as fuel). If we can lase it hot enough to double the exhaust velocity, the rocket equation says we only need about a square root of the original amount of propellant and power, because almost all that fuel was lifting the rest of the fuel.

To move from the 85% propellant of rockets to 15% (somewhere between a fighter jet and a train, according to the article) we have to increase exhaust velocity of whatever we're pushing down to push us up by 12x.