I'm not quite sure what you mean by saying that the Japanese road network is not a grid. In terms of actual layout, it's quite grid-like. I would even say it's usually much closer to a nicely laid-out grid than the mess any European city is.

What Japan lacks are addresses that can be found easily without using a map. Apart from Kyoto, roads in Japanese cities don't have names (or number), so addresses within cities are not "{number} {name of street}". Cities are cut in areas smaller and smaller all the way down to a block. The last number will be the house on that block. So addresses within cities are "{name of area} {sub-area number} {block number} {house number}", with some variations from city to city.

An address might be "Nantokacho 11-16-8", which means the 8th house around the 16th block of the 11th sub-area of the Nantoka area. Good luck figuring that out without a map!