How was Snape killing Dumbledore an act loyalty in Harry Potter and the Deathly Hallows?

There are various possible
interpretations.

One possibility is that Dumbledore
suspected that Draco would be put in such a position, with Lucius's loyalty in question,
and due to Snape's closeness with the family, it's possible that Dumbledore asked Snape
to watch over him. The Malfoys, with the help of Bellatrix Lestrange, made this a
permanent position by asking him to make the Unbreakable Vow. Without question, Snape
told Dumbledore about this, and Dumbledore probably requested that Snape maintain
Draco's innocence.

Alternatively, it's possible that
Dumbledore had some inkling about the role Draco would play later--with the wand
switching authority and so forth. However, it is more likely that the old wizard was
concerned with maintaining Draco's innocence.

In killing
Dumbledore, Snape did as was asked of him (as it can be assumed), and his murder was
therefore an act of loyalty.

Additionally, outside the
interpretation of the story itself, in terms of literary devices, Harry Potter's story
is a quest, and in quests, the hero must go it alone at the end. It's why Harry goes to
the forest by himself, without Hermione or Ron, and why the majority of the adults who
helped him along the way had to die (Sirius, Dumbledore, Mad-Eye, Remus, Tonks, Snape,
etc.). In effect, Dumbledore had to die, so Rowling relied on this to develop Snape's
plot and provide him a role as a hero.