Is anyone successfully running a windowed emacs, (not terminal emacs), on one of the new Mac M1s?
Does this port work? https://emacsformacosx.com
Is there another?
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Yes, https://emacsformacosx.com works on the M1 Macs. However, it does also require that you override the security preferences regarding app identity when you have downloaded and installed the package, immediately after running it.
Editorial note: because I don't have 50 reputation, I am not allowed to comment on the answer, which I believe already answered the question. I think it would have been more appropriate to comment with a clarification, rather than having to enter a completely new answer.
Yes. The Emacs from macsformacosx.com works in GUI mode on the Mac M1. It is running in x86 emulation mode, not native ARM mode, but it works.
I plan to try some of the other versions later (Mitsuharu's version, homebrew version, nativecomp version) but since this one works I'm going to use it for now.
You can use this repository  and install Emacs using brew. I think the README is self-explanatory. I use Emacs Doom as IDE with heavy reliant on LSP. This Emacs source has some needed patches to make it work on Apple ARM machines.
I have this working as well, from both the dock UI and commandline entry points. To get the commandline entry point to work, I had to run emacs from a rosetta-enabled terminal, e.g.
In that terminal, start up emacs like this: