As I understand it, Pacts are an exception to the Missed Trigger rule; if a Pact trigger is missed, no matter how far the trigger has gone, the game is considered over and the Pact controller loses the game. I believe this is a special exception to the missed trigger rule. Is there a similar exception for other effects which would cause a game to end? E.g.:

- Player at 1 life misses a Phyrexian Arena trigger.
- Player with no cards in library misses a Howling Mine trigger.
- Player with 250 cards in library misses a Battle of Wits trigger.

Apologies for not using card tags; it's kind of unwieldy on mobile :(

You are putting too much emphasis on the “lose the game” portion of the trigger, and not the part that matters.

The part that matters is that it is a trigger with a “default” action, like Echo or any “Do X, unless you do Y” type trigger
In those cases we resolve the default action. See the IPG for exact timing.

———————————————
This space intentionally left blank

With pacts they are optional to pay for them. If you cannot they have a default action of “lose the game”. This is defined in the additional remedies section, first paragraph.

Ah, my bad. For some reason I thought there was a special exception at play here. Thanks guys!