Link: http://www.mediafire.com/file/jfw612npc9fg4pp/DirecTVNow_beta_2.0.10.06114_modified.apk
This version is modified to not include the Amazon Store App requirement. So just uninstall old DTV now and Amazon Store apps, sideload this new app, login, and you are good to go.
Works like a charm on my shield.
Please credit ACHILLES R32 from XDA forums for taking the time to modify and upload these updates for the rest of us. You da the real MVP.
I put in my login and password, select "Accept the AT&T terms" (or something similar), then get..
"Sorry for the inconvenience, please try again later."