Turkish Airlines complaint: Gate was closed before the time, we were charged for 2100$ instead of 210$

Hello,
On 1st July we arrived to the gate no D16 for the continuous flight Istanbul – Bangkok
1. The flight was delayed couple of times till 17:50 – please see a picture no 1

2. I was not noticed either by email nor by SMS/text message about the schedule changes as it supposed to be according to the Turkish airlines policy published on WEB:
https://www.turkishairlines.com/en-int/any-questions/flight-cancelations-and-change-questions/index.html

3. We arrived to the gate at 17:28 (22 min before the flight). The gate was already closed (2 minutes ahead of time) and we tried to get help from the staff that was in gate. After 3 minutes of trying, and getting negative answers although we came on time, we took a picture where you can clearly see the gate, the time and the employee– see pic no 2
4. Although on the flights screens the flight was appeared as 17:50(as shown at the picture no 1) , in actual on the gate it was 17:40 , and we haven’t seen this 10 min additional change neither on the digital board that was screened at the airport and of course not mentioned a personal sms / phone call/ email to on that as well , we assume it was changed in the last minute while we were on our way to the gate.

5. After we were refused to get boarded to our flight, we went to Turkish airlines desk to get assistance, which we needed to wait more than 45 min – in this urgent situation , no sensitive/empathy to our critical situation from the staff.
6. They told us that we are right but there is nothing they can help (after we waited so long).
7. According to the Turkish airlines policy published on website, we supposed to be 20 min before the flight – see screenshot taken from the website

8. We were at the gate 22 min before the flight
9. At the Turkish airlines desk, after showing all evidence, I was totally surprised that instead of compensating us because the gate was closed earlier than is supposed to be closed, the desk officer told us that we must be charged in order to exchange the flight
10. Since I bought the flexible tickets(I have paid extra 105$), in case of flight change and according to the written in tickets policy, I supposed to be charged for 69$ per person, which means around 210$
11. Somehow the charge was done for around 2100$
I would like you to the your internal investigation , as I already provided all the supporting evidences for the case which were not align with Turkish airlines policy.
I’m requesting a full refund of 2100$ that was charged .