She ran down the stairs.

Literal

She [topic-は] stairs [path-を] ran-down.

駆け下りる is a compound verb fusing 駆ける ('to dash, race') and 下りる ('to descend'). The first verb supplies the manner (running, at speed), the second the action proper (going down). Compound verbs like this are extremely productive in Japanese — 飛び降りる ('jump down'), 走り出す ('start running'), 立ち上がる ('stand up') — and are how the language packs adverbial nuance into a single lexical unit. The を on 階段 marks the path traversed, not the direct object — a special use of を with motion verbs (cf. 公園を歩く, 'walk through the park').