specifically what "laser weapon system" would that be?
Well, the wording on that is not really very proper...they do not have such a system ready yet.
The point is that they may be preparing the new Atago with the type of power output they would need to power one, either of their own or from the US or elsewhere among allies.
Japan's Technical Research and Design Institute with the Japanese Defense Ministry has been working on Laser Weapons Technology for some time, as well as the work being done in Osaka and elsewhere, including a number of private technology and military contractors..
As I said, there is a god deal of thought about the advanced Atago and its power, as to whether it was upgrading its power capabilities to allow for future laser and rail gun type weaponry.
At the same time, Japan's been having some success in the defense industry and prvate industry with laser research. For example in 2015, Japan's Laser for Fast Ignition Experiment (LFEX) test in Osaka had some significant success in 2015 but it was not weapons grade or caliber...but it did provide some significant research and technological advancement..
JApan is also woking with Lockheed, Grumman, Thales, and others on their development.
Time will tell...but Japan is definitely working on these programs...both with US defense contractors, and on its own.