'Now their watch is ended' carries all the meaning of 'Now their watch has ended' with the further implication that by the act the speaker has just accomplished or observed is the watch ended.
have as an auxiliary verb:
"As in the other Germanic (and Romanic) languages, the various moods and tenses of have are used with the past participle of another verb, to form a series of compound or ‘perfect’ tenses of the latter..... [The entry explains how the use of have as an auxiliary developed from its meaning: to possess] .... Verbs of motion and position long retained the earlier use of the auxiliary be; and he is gone is still used to express resulting state, while he has gone expresses action. See BE 14b".
be as an auxiliary verb:
"[Be is used as an auxiliary verb] in intransitive verbs, forming perfect tenses, in which use it is now largely displaced by have after the pattern of transitive verbs: be being retained only with come, go, rise, set, fall, arrive, depart, grow, and the like, when we express the condition or state now attained, rather than the action of reaching it, as ‘the sun is set,’ ‘our guests are gone,’ ‘Babylon is fallen,’ ‘the children are all grown up'."
I think it is the use of 'to be' rather than 'to have' that lends it the weight and finality.