First, the seat map may not at all reflect the number of people booked on the flight. People may be booked but not have seats assigned yet for any number of reasons.
That said, airlines seek to maximize their profit, not to fill the plane. If someone is booking a flight at the last minute, there's a decent chance that particular flight is important to them, so they are willing to pay more. Last minute travelers might be bargain-hunting vacationers looking for a good deal, but they might also be business travelers who need to attend an important meeting and will do so at any remotely reasonable price.
As an example, the airline can make the same revenue (approximately, because of ancillary revenue from things like baggage fees) by selling 10 tickets for $100 or one ticket for $1,000. Which is easier: finding a single last-minute business traveler with limited budget constraints who absolutely needs to get to Istanbul or finding 10 bargain-hunters who are prepared to go to Istanbul at the last minute?
The airline's revenue management team has spent a lot of time answering this question, and they have decided that they think they can make more money trying to get a smaller number of passengers to pay more for this flight than if they tried to get a larger number of passengers to pay less. As such, they've raised the price.
And the airline may be more clever than that. They might sell the seat to the last-minute business traveler for $1,000, while offering a cheaper fare to a traveler who stays over the weekend, who is probably a vacationer with a more limited budget. Or, in some cases, they may sell the ticket for $1,000 normally, but offer it at a lower price through an opaque booking engine like Priceline or Hotwire to specifically target budget-conscious travelers. In this way, they can do their best to maximize revenue by having it both ways: sell seats at a low price to those who are price-sensitive, without cannibalizing their ability to sell seats at a higher price to those who are not.