I mistakenly posted this inside your quote when I replied so it may have been missed so I am re-posting it and deleting my prior post. But I think this explains why the Washington loss mattered to Dallas:
The answer is if Washington won and Washington, NY and Dallas wind up tied with Seattle and Detroit, at 10-6-1, Dallas would lose the division tiebreaker to Washington. Had Washington won they could finish with a division record of 3-2-1. Dallas could finish at 3-3. The tiebreaker rules start with deciding divisions ties first. Washington would eliminate NY and or Dallas in a tie breaker based on division records. Then Washington moves on to a tie breaker with Detroit and Seattle. Now Washington ca only finish with a 2-3-1 record in the division.
Of course this would be an incredibly unlikely scenario but it was possible. At this point, with Washington losing there is no circumstance where Washington wins a tie breaker over Dallas no matter what happens. Washington can pass Dallas in the standings by winning out, (NY can pass Dallas by winning 2 more games). Dallas can actually finish last in the division still and make the playoffs winning tie-breakers over Seattle and Detroit. They need a win or tie to clinch 2nd place and the 5th seed.