That's a fair description I'd say, but I'd try to think more about it in terms of how sets of edges are arranged.
Basically, in 1-point-perspective the image is arranged in a way, that there are only 3 types of edges. 2 types that are perfectly parallel to the image plane or viewer, going up and down and to the left an right. The other type are edges that are perfectly perpendicular to the image plane, so they'll point straight away from the viewer.
The first to types are the easiest, since they have no perspective and will be either horizontal or vertical lines in your image. That means that in it's simplest form (so no tilted edges), ALL lines that are not perfectly vertical or horizontal would be point towards the single vanishing point.
And that's basically what I'd focus on the most in 1-point-perspective: Make sure, that all lines, that are neither vertical nor horizontal converge to vanishing point, which is the common point of interception for all those lines). To really reinforce what I am trying to say: If you'd extend all lines that are neither vertical nor horizontal to the horizon, they'd all hit a single point. That is the vanishing point.
In your image it kind looks like you kind of know this concept, but use it more like an approximation. No blue lines, only red lines! =)