The usage to be [some amount of money] out is a (significantly less common) alternative to colloquial to be [some amount] down.
down (Cambridge Dictionary)
in or towards a lower level, a smaller amount, or a simpler state
Ex. The Cavaliers were 20 points down (= losing by 20 points) at half-time.
But it's worth pointing out that the down version is also used for other "quantifiable values" (often, but not always, in contexts where lower = worse, higher = better).
It's also worth noting that the out version is almost exclusively reserved for contexts where the "amount" is either money or something that can easily be seen as having a monetary value. Also, that it nearly always implies a money / value that the subject previously had, and has now lost.
Another usage difference is that Bear Grylls would have been extremely unlikely to say I am out 15 feet (in the more "literal" sense of out = away [from some initial starting position.
But for the out = without [having lost something] sense, the sequence I'm out £10 is far more common than I'm £10 out - whereas I'm down £10 and I'm £10 down are equally common alternatives.