Whalton was about to witness the tragic ending of a desperate chase in the waters off what was then the US Territory of Florida.

此 off 非 of 之意！

off 表示位置关系。意为两个事物“离开；不接触，在附近”。

in the waters off what was then the US Territory of Florida.：在美国佛罗里达领地附近的海域（水域）

what was the US Territory of Florida = the US Territory of Florida

in the waters off what was then the US Territory of Florida = in the waters off the US Territory of Florida

off the US Territory of Florida 作 waters 的定语，把蓝色的词组理解了，就OK了。