Usually the sender pays the fee, the minimum fee is based on a complex formula that I don't know completely, but it's based on the number of inputs to the transaction. More inputs means more space needed in the block to represent the transaction, and blocks have limited space.
What has happened recently as the article says, is as the amount of available space in each block has diminished (due to more transactions), even single input transactions have needed higher fees, otherwise they get left out of the block (in favour of other transactions that did set higher fees). So then a marketplace opens up where people 'bid' to get their transactions included by adding more fees.