I was going to post this to get help, but figured out the answer and since I couldn't find the answer anywhere else, I'll share what I learned for other's benefit.
I logged in to my camera on a new Mac today and the video player showed a link to "Click here to download and install took me here: https://support.amcrest.com/hc/en-us/ca ... in_242.pkg, which was an invalid address and thus redirected to the general download page. Unfortunately that page provides no links to download the plugin.
On a whim, I checked to see if my firmware needed updated (not easily found on the Amcrest site either as they only provide a link to a confusing page that asks you to register your email address every time you visit to download firmware). After registering my email, I found there was a July 2017 update (I had March 2017) that included a fix described as "Fixed minor MAC plugin issues".
Installing this update fixed my plugin download problem. In Safari the link now downloads the plugin from a new location (https://s3.amazonaws.com/amcrest-files/ ... n_alps.pkg as of April 2018). In Chrome, it says the same thing about downloading a plugin, but when clicked redirects to the Chrome Store with a link to launch the Chrome web viewer (not as convenient in my opinion).
I hope this saves someone some time.