You might want to be a little more detailed on the "import the GPG key" step. After you import the the key and see it on your list, you need to right click on it and select "Certify Certificate". That brings up a list of certificates for Alan C. Reiner. On my system there were three of them. I'm not sure if all 3 should be selected or just the one labeled (Offline Signing Key). I opted to select just that one. Then at the bottom of that dialog box is the key fingerprint which you should carefully examine and make sure it matches the expected fingerprint given on the web site. Then select the "I have verified the fingerprint" box and click next. Then it asks if you want to verify it just for yourself or verify for others. Select the box for verify for myself and then accept.

After the key is verified, then you can verify the checksum file by right clicking on it and selecting "Decrypt and verify". However, the dialog that comes up had the "Input file is a detached signature" box checked by default. If I left that alone, it did not work and I'd get a "no signatures found" error. However, deselecting that box before pressing the "Decrypt/Verify" button resulted in a successful verification. It also created a new  file named armory_0.90-beta_sha256sum.txt in the directory beside the .asc file with the SHA256 signatures but not the GPG signature.

I hope that helps a bit.