It was a double bluff.
It seems to be being forgotten that it was his money to do with as he pleased. That would have been true whether he'd shredded it or not.
The point, though, is that right until he 'admitted' that he hadn't shredded it but given it to charity, David Beckham was unmoved, and did nothing in response. He could have stepped in, offered to match the money, agreed to make some sort of statement about human rights in Qatar, or something, but he didn't. Arguably, that would have been giving in to blackmail, but the counter-argument would be that it was an offer of payment to use his influence, and DB is far from averse to that sort of deal. Maybe £10k was too much like small change for him?
Had JL said at the start that he would donate the money whatever happened, the stunt would have been a damp squib. This way, DB (and the other 'stars' who are acting in support of the Qatari regime) has been exposed as a hypocrite, JL has gained publicity for himself, and the money has gone to charity, so I see it as a win all round.