It's misleading to look at transaction fees as a percentage. Bitcoin transaction fees are based on the size of the transaction in bytes, regardless of the value being transacted.
According to the site you linked,
The fastest and cheapest transaction fee is currently 0.0000042 BTC/byte, shown in green at the top.
For the median transaction size of 226 bytes, this results in a fee of 0.0009492 BTC.
If you are trying to send BTC 0.005, then yes, that is about 20%. If you are trying to send BTC 0.5, then this will correspond to a fee of about 0.2%. For comparison, credit cards typically have a fee of around 3%.
Is anyone still using BTC?
Obviously yes. Transaction fees are based on supply and demand - the network only allows so many (bytes of) transactions in each block, so fees are effectively bidding for space in a block. If "nobody" was using Bitcoin, you would see fees become very low.
Note that there are several current proposals for increasing the block size, or otherwise allowing a higher volume of transactions on the network. If and when any of those take effect, fees should come down.
Maybe I'm doing something wrong here but after some checks on https://bitcoinfees.21.co/ and blockchain it seems that those are the real fees and people just keep paying them. Why?
Because paying a high fee to spend Bitcoins may still be better than not spending them at all?
See also Is it normal to not "own" your bitcoins? Are 6% transaction fees normal?