The bitcoinfees.21.co website, and mostly everyone's brain, is broken.
Look at the graph on bitcoinfees.21.co, it's pretty clear to see that 120 satoshis per byte is what you need to pay, no different to last week. Or last month.
No it isn't. Fees of 120 satoshi/byte can leave the transaction unconfirmed for several days in most or at least many cases. Note that on the site it says 5 blocks to infinity and half the transactions sent with those fees are not confirmed. A lot of people send fees of that size, but a large portion of that is ignorant Blockchain wallet users and other newbies who didn't choose a wallet with decent fee estimation.
Sure, a transaction doesn't really need to confirm within the next block so you don't actually have to pay fees quite that high, but even 220-240 satoshi/byte fees often take an hour or so. Litecoin transactions are much cheaper because the blocks aren't all full.
It's a spam attack, but they're definitely capable of keeping it going for long enough.