These textures are normal maps. They are used to fake details on otherwise low-poly models. Yakuza mainly uses two types of normal maps: yellow normal maps and green normal maps.
Yellow normal maps are the most common in Dragon Engine games, and green normal maps are the most common in Old Engine. Both engines support both types of normal maps. It also supports the standard purple normal maps.
Green normal maps store the X+ axis in the alpha channel, and store the Y+ axis in the green channel. Yellow normal maps store the X+ axis in the red channel, and store the Y+ axis in the green channel. Ishin Kiwami's green channel is in the Y- axis. The Z+ axis is calculated in the shader with this shader code:
//Remap normal map to -1 to 1
normalMap.x = 1 - (2 * tn.x);
normalMap.y = 1 - (2 * tn.y);
// Dot product of the vector (normalMap.x,normalMap.y) and itself, multiplied by -1 and then added by 1. Then, pick the largest number between the result of that and 0 (so that the result never becomes a negative number), and square root it.
tmp.z = 1 + -(dot(normalMap.xy, normalMap.xy));
normalMap.z = sqrt(max(0, tmp.z));
The engine can differentiate between green and yellow normal maps by reading the header of the .DDS file. If the .DDS file's header is "DxT5xGxR", it reads it as a green normal map.
For assets they usually end with the prefix "_n".