She's rich, but he's twice as rich as she is.

Literal

She [topic-は] rich is [but-が], he [topic-は] her 2-times rich is.

その2倍 refers back to her wealth ('that amount, doubled'), with その working as a deictic pointing to the previous clause. The multiplier ~倍 attaches directly to the number, and the whole 'twice that' phrase modifies 金持ち without an additional particle — the result is dense but parses cleanly: '(he is) her-2x rich.' This kind of comparative cross-referencing within a single sentence is a useful Japanese construction for relative quantitative claims.