the site relies on client-side javascript being executed correctly... and it seems to not do any checks on the server side. so someone seems to have not taken web design 101.
I just gave myself a balance of 123.456 and there are others with way higher balances, would be really cool if it paid.
they will probably see you didn't make high scores and deny your payment
Probably...
But it's also relatively simple to send a full, valid, and plausible history of a game that goes to 16384 because they don't transmit the seed for the random number generator, so you basically have free choice of placing the next tile. And even if they would transmit it, you could still calculate everything in advance and then choose the best strategy to have a high chance on 16384.
Also, if you just want to rely on AI without modifying the code on the site, you can easily get 8192 in a few seconds, if you're lucky also 16384 after a few tries.
So it remains: Never gonna work, best not waste time, there are websites with much fewer ads where you can play 2048 :p
[edit]
there are tons of strategies for 2048, google is your friend.
