Is it normal for cats to periodically vomit dry food?

It is not normal, although it also doesn't seem alarming.

Cats usually vomit furballs. If you only see dry food, it is not the usual vomit.

The usual cause is cats eating too much dry food and then drinking water. Dry food expands with water and might be disturbing their stomach. This theory has more credibility since the puzzle feeder helped it.

My suggestion is to reduce the availability of the dry food. Feed them more frequently with less food to see if this further improves the situation.

Disclaimer: I am not a vet.

C.Koca is spot on with expanding food. Dry food with a high grain content expands more that food with a high meat content, so switching brands might help. Please keep in mind that grain content is proven to increase the risk of urinary tract diseases in cats and that male cats are much more prone to those stones than females, so switching food might be a good idea in general.

A second possible cause is a sensitive stomach. One of my cats had similar problems with vomiting food that very slowly got worse and worse. We switched to a "sensitive" dry food that was very oily and the problem disappeared.

Yes, it's normal. Search "cat vomit food" and you'll find vets suggesting 1-3 cat upchucks a month is normal, but to only worry if it's twice a day for several days in a row, possibly with blood.

My cats seem to barf up some dry food at least weekly, and have been in fine health for decades (combined). It wasn't the food, since the other 6 days of the week are fine. Some of it seems to be nerves -- if they see a scary dog or something -- some is the food being in front of a hairball (which is not a ball), but cats also barf for no obvious reason.