Server list should have only one to chose - Global. WIN Registry issue. Try reinstall again. After uninstall make sure in REGEDIT that Blizzard and BattleNet sections are empty of war2 gateways entries.
There is almost not one who play on official Global. Going to zero. Although a very few ppl online at weekends.
You can download reg file with gateways for war2ru server. Their reg file also contain official Global adress so you wont lost access to it (you can add any addresses there, including currently stored in registry EAST/WEST/ASIA/EU).
Go to http://en.war2.ru
/ downloads section.
GOG installer put Global address at finishing of installing. Removing registry entries for war2 (eg for ingame settings reset) erase Global and game at next launch restore older 4 servers instead of Global.
For GOG Galaxy build you can verify game installation and Galaxy restore registry entries.
Reg file (some backup or file from war2ru) or full reinstall for GOG offline build.
If Galaxy not repair it - it is security issue. Reinstall every thing, flient to to D/Games/GOG/Galaxy/, games to X/Games/Game-name/.
Still for games updating/downloaeing/verification-installation start galady.exe as admin. Use armin for the first game launch or just start it after downloading(*) directly from Galaxy (adminrun will be applied to all daughter process).
*Force verification, at least twice, after initial game downloading. After verify start game directly from Library.
Next you can restart Galaxy without adminrun or restart game from Deaktop link without adminrun.
In any case non-system drive installation still mandatory, alaye, any game and client, installlocation and adminrun.
Adminrun is mandatory for install and first run same way - in any installlocation.
Originally game use HKLM with partially switched to HKCU sections of REGEDIT. That mean some arguments after second game launch will be restored to defaults from HKLM section since Windows create and force game to use HKCU/ VirtualStore copy of HKLM. Shouldnt be any issues play game without admin rights as result. But if you use some reg files - if it refer to HKLM section double it to HKCU and/or VirtualStore.
If you not use Galaxy first adminrun can be from Desktop link or directly from War2aLauncher.exe. Point is Launcher arguments (aemin, cpu priority, compatibilities) applied automatically to war2.exe just like every else parent process do in Windows OS.