Looks like gproxy closes after w3 starts. Turn on Debug flag for groxy and provide full log again.
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] starting winsock
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] setting process priority to "above normal"
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] Listening for gproxy games on port [6125]
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] Listening for warcraft 3 connections on port 6112
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] GProxy++ Xpam Version 13
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] List of commands: !commands
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] GPROXY READY
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] Waiting max 25 seconds for W3 to start
[19-08-2017 15:11:10][SYSTEM][LOG_INFO] Waiting W3...
[19-08-2017 15:11:11][SYSTEM][LOG_INFO] Detected W3 as running
[19-08-2017 15:11:11][AMH][LOG_DEBUG] amh init
[19-08-2017 15:11:31][AMH][LOG_DEBUG] Process32First
[19-08-2017 15:11:31][AMH][LOG_DEBUG] GLE:
[19-08-2017 15:11:31][AMH][LOG_DEBUG] [System Process]
[19-08-2017 15:11:31][AMH][LOG_DEBUG] Opened w3 process
[19-08-2017 15:11:31][AMH][LOG_DEBUG] Failed to find module
[19-08-2017 15:11:31][AMH][LOG_DEBUG] Init failed
[19-08-2017 15:11:31][AMH][LOG_INFO] EXITED
[19-08-2017 15:11:31][SYSTEM][LOG_DEBUG] AMH thread exited
[19-08-2017 15:11:31][SYSTEM][LOG_INFO] Shutting down
[19-08-2017 15:11:31][SYSTEM][LOG_INFO] Shutting down winsock
[19-08-2017 15:11:31][SYSTEM][LOG_INFO] GPROXY EXITING
Requested patch: stable
No newer patch exists. Xpam is up to date
Update finished
Client update finished
Client is up to date
D:\asus kurtarma\Warcraft III\Warcraft III.exe
W3 is up to date
Checking if DotA map exist: DotA v6.85k Allstars.w3x
DotA v6.85k Allstars.w3x exists.
GProxy is ready
D:\asus kurtarma\Warcraft III\Warcraft III.exe
GProxy is ready
D:\asus kurtarma\Warcraft III\Warcraft III.exe
D:\asus kurtarma\Warcraft III\Warcraft III.exe