There are a couple of things going on here for you, one is a misunderstanding of how snaps work. Snaps are intended to snap to other snaps, they are attracted to each-other like magnets within your model. In order for your setup to function the way I believe you intend it to you would need to have a corresponding snap built into your pipe as well. These two snaps would be best placed on the radial center of the flange and of the pipe, with their front sides facing outward and with their clocking set to a cardinal point of circle they are centered onto. When snaps come together they also rotate the object they are attached to by aligning the clocking of the two snaps. Also, a side note that snaps must be in the first level of a multi part component, not nested within a sub component.
To activate a snap you need to grab the item in question using the move tool BY THE SNAP. Then the snap will start looking for other snaps, if you press ALT on Windows or Command on Mac after picking up somthing by it’s snap you can activate a visual tractor beam that will show you adjacent available snaps.
Here I have set up a set up your flange and the pipe with snaps on their center axis. I pick up the flange by the snaps and hit the modifier key to activate the tractor beam, this is not necessary as snaps will snap together without it just the same but it helps illustrate what is happening, and can help find a snap in your model. If you work regularly with these components you might set them all up with such snaps.
So, because it takes two snaps to tango, in your example model the snap you have is doing nothing, it’s acting similar to the way any other inferencing point would. What you are seeing is the action of inferencing engine in SketchUp at work, and any point you grab from will behave similarly, looking for other inferencing points in the model as you move around, they could be faces or nodes or midpoints or guides or edges, all of these trigger inferencing points all the time even without any snaps. Whats more, after invoking the move tool you can press the modifier key to cycle through various sets of handles that are available to grab an object, one of which is component center. As a quick example, here I grab the flange by its center and move it to the center point of a pipe using the move tool alone and the inferencing engine without any snaps. First I toggle the handles on the flange to find the center handle and grab it by that, then I hover over the edge of the pipe OD circle telling the inferencing engine I would like to find it’s center, then I move to center and click again.
So, your purpose can be achieved without snaps if it is occasional, this could also be achieved using guidepoints or facilitated by turning on hidden geometry temporarily to see the outside edges of your pipe for inferencing. But if you do this very frequently it might benefit you to build a personal library of components that have snaps to make things quicker. Here is some further reading: