Thanks to everyone who responded to this. I emailed ESPN, and here is their response:
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Hello,
Thank you for contacting us.
Due to rights differences, Monday Night Football is only available on WatchESPN on a desktop, WatchESPN on XBox with a XBox Live GOLD membership, or on the WatchESPN application on iPads. iPhones and Android devices will not have access to Monday Night Football programming.
For live assistance with this or any other issue, please call Customer Care at 1-888-549-3776 (ESPN) between 8:00 a.m. and 1:00 a.m. EST.
Regards,
Sam
ESPN.com Customer Care
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Looks like they have made an arbitrary decision to allow it on desktops and XBox with subscription, and curiously, only iPads. Not available on iPhone or any Android device. Still doesn't make any sense, but it's their content and they can make their own rules.