So I finally got it running, at least in a crippled form. I am using the php -S localhost:8000 means of running it. That requires excluding all the javascript tests.
$CFG->behat_wwwroot = 'http://localhost:8000';
Then in one terminal window, I ran:
php -S localhost:8000
And in the other window I ran:
php admin/tool/behat/cli/util.php --enable
vendor/bin/behat --config /local/behat/behatrun/behat/behat.yml --tags="~@javascript"
It appears all the tests are failing. It appears they can't get past any kind of PHP notice errors. Well, that's at least something.