Not quite on topic of Gnocchi...but for potato ricers.

I don't use it for potatoes..I just don't care for super creamy mashed potatoes.
I do use it for squeezing out moisture of spinach..and for cole slaw. Salt the slaw first rinse and squeeze with the ricer and let it dry a bit and dress it so it soaks up the dressing better...and is crispy.

YES ! It makes potato "snow" with no risk of the potatoes getting gluey and tacky, or leaving them too chunky. A food processor or mixer will give you the former, a masher will give you the latter.

The ricer or a food mill work very well the amount of flour you use is important but also the tool you use for the potatoes is also as important

I'll add my voice to "yes" on the ricer. I really do think that it makes a difference. Also once you've mixed in the flour you need some skill in rolling out even width "dowels". One of my friends is expert at that part. After that you slice them and then flick them off your gnocchi form.

I agree to use your 'ricer' - to make it nicer. Gnocchi is all about texture and getting the right ridges to hold the sauce.

Well, i think that a ricer helps to aerate the potatoes so that they dry out easier before you add the flour -- so you don't need to use so much flour to make the gnocchi (which is important for gnocchi texture as HalfPint said above). I think a food mill would work too for this. Or you could mash them with a masher and put the mashed up taters on a big rimmed backing sheet so they would have a good surface area to steam off the moisture.

I would say yes. since you don't want any actual chunks of potato in your gnocchi dough, a ricer is a great way to ensure you get a fluffy, completely chunk free potatoes.

IMHO, no, what is important is the amount of flour added. Too much has the gnocchi is chewy and heavy. Too little and they fall apart when cooked.