I guess you are referring to
The Amtrak "packing your luggage" page.
I normally carry one or two LL Bean rolling duffle bags which are made of woven nylon and have zippers and it has never been a problem. I see lots of similar bags on the trains, and don't remember ever seeing anything that said they aren't allowed.
I think the "woven fabric zipper bags" refers to the third picture, which appears to be a reusable shopping bag with a zipper closure, not a bag (like a duffle bag) designed to be used as luggage. The second picture, which shows a soft-sided roller suitcase, is problematic because it is not closed and the contents are falling out, not because it is soft-sided or zippered. It falls under the "containers that cannot securely hold their contents" provision. The zippers are broken or it is so overstuffed that it can't be zipped.