Well, that solves his worries about how to introduce himself. He'd run right into him. There's no real question of who this is-- Giles has a whole file, picture included-- and then a vampire in its demonic visage barrels right after him, and Giles yelps in a very undignified way and stumbles back.

"Wait!" he calls out futilely, frantically digging into his bag and unearthing a stake, fumbling it into a defensive position. "Come back, you-- you need this--"

The fact that Giles hasn't run and is instead dawdling around makes him a prime target for the vampire, who slows, then jerks to a halt, conflicted between his revenge and this seemingly soft target of an old man. Giles isn't quite that helpless but he's only the Slayer's trainer, not the Slayer her-- err, himself. It's hardly the same.