You'll see that your client keeps trying to connect to 220.127.116.11 on TCP 7255 until it finally resets at 31.74 seconds in. This is where it times out and tried again.
There is an initial setup on the SYN, SYN - ACK, ACK that incldues
What I'd like for you to do is when the launcher is running and it keeps trying to connect try to telnet on 7255 to the patch server. Run your packet capture while STO launcher is repeating the connection attempt and your are trying the telnet connection.
Telnet port test
From a command prompt (Start - Run - Cmd) telnet to the patch server to see if the TCP port is open. You can install telnet client if it isn't on the system easily.
By default, Telnet is not installed with Windows, but you can install it by following the steps below.
To install Telnet Client
1. Click the Start button Picture of the Start button, click Control Panel, click Programs, and then click Turn Windows features on or off. Administrator permission required If you are prompted for an administrator password or confirmation, type the password or provide confirmation.
2. In the Windows Features dialog box, select the Telnet Client check box.
3. Click OK. The installation might take several minutes.
So we know that your PC, at the Wireshark capture level, is showing that you aren't getting the DATA packet replies back from Cryptic. 18.104.22.168 TCP 7255 to your internal IP and port with a PSH, ACK reply.
If you happen to have a hub (not a switch, but an old hub) and another PC/laptop available with a wired network adapter you can do a promiscuous packet capture to see the traffic outside of the STO PC.
The STO PC is connected to the hub on a port
Your 2nd PC/laptop is connected to the hub on a port
The hub is connected to your modem or router on the LAN side
You install Wireshark with WinPcap on the 2nd PC. When you run the packet capture you use promiscuous turned on so you see all traffic on the hub.
If you see the PSH, ACK traffic on the capture from 22.214.171.124 to your STO PC IP, you know that something local to the PC is blocking the connection. If you don't then you know something at your router / modem or ISP level is blocking that return traffic from Cryptic.