The word chosen by the documentation is a bit confusing.
It says “Opposite of the value of X on the K-means objective.”
It means negative of the K-means objective.
K-Means Objective
The objective in the K-means is to reduce the sum of squares of the distances of points from their respective cluster centroids. It has other names like J-Squared error function, J-score or within-cluster sum of squares. This value tells how internally coherent the clusters are. (The less the better)
The objective function can be directly obtained from the following method.
model.inertia_