A better circle test would’ve been one where the laser travels in a circle, instead of what’s in the picture - an image of a circle drawn horizontal lines.
The horizontal line method has the Y axis moving in the same direction, so the backlash is hidden.
The X axis does appear to not have backlash, but it’s hard to see because of the adjacent partially overlapping passes. A single line would be clearer.
Here’s when I did this with varying backlash compensation settings, you can see a distinct shift in the circle. In this case I had approximately 0.12mm of backlash in the X axis after a crash, worth correcting as normally it should be about 0.02mm.
That FAQ article you found would be the steps to follow if linear modules are found to be wobbling. I really don’t like how it’s phrased in the article, as it calls out numbers that are nearly impossible to measure. It’s more straightforward to adjust it until you can just barely insert the carriage between the rails (a small amount of preload required to force it in), but it rolls smoothly without effort once inserted. If there’s no force required to insert the carriage onto the rails then it will still have a small amount of slop.