In the nomination process, TAR usually submits one episode for consideration in the technical categories, but for the series category, it's basically a popular vote and name recognition. Voters are not required to watch a single episode to vote in the series categories. But shows will of course encourage voters to check out their show (though magazine ads, billboards, etc) and with everything online now, entire seasons are made available.
(In the past when a DVD mailer was the main way to campaign and get a show out there to voters, reality shows would highlight one episode and that one episode held much more importance before than it does now.)
After nominations, comedy and drama programs submit 6 episodes that voters are technically required to watch before casting their vote. But that rule is not strictly enforced and it is all based on an honor system. I'm not sure if reality-competition programs also submit more than one episode during final voting. But if it's only one, then it'll be that episode submitted for consideration in technical categories from the nomination round.
Also, any eligible Emmy voter can, but is not required to, vote in series categories. And the big change last year, which actually might disadvantage TAR, is that winners are chosen through straight voting and a nominee wins based on plurality. So a program can win with as little as 17% of the total vote. Previously, it was a preferential/ranked ballot and voters would rank the nominees. The one with the lowest score (most #1 and #2 ranks, for example) would win. TAR could very well have benefited from being ranked high on most voters' lists, even if not ranked 1st.
Another interesting note about this year's Emmys is the introduction of Outstanding Casting for a Reality Program category. TAR was not nominated.