It's clear from the output of ProcMon (edited) that the current path is not being searched. Instead the dependency is assumed to live in its own folder in the main game installation folder...
16:46:27.7771128 arma3.exe 10892 Load Image D:\Users\user\Documents\Arma 3 Alpha\Arma3TestExtension1\Arma3TestExtension1.dll SUCCESS Image Base: 0x16440000, Image Size: 0xb000
...
16:46:27.8619788 arma3.exe 10892 QueryOpen D:\Program Files (x86)\Steam\steamapps\common\Arma 3\netStuff.dll NAME NOT FOUND
16:46:27.8620583 arma3.exe 10892 QueryOpen D:\Program Files (x86)\Steam\steamapps\common\Arma 3\netstuff\netStuff.dll NAME NOT FOUND
16:46:27.8621299 arma3.exe 10892 QueryOpen D:\Program Files (x86)\Steam\steamapps\common\Arma 3\netStuff.exe NAME NOT FOUND
16:46:27.8622006 arma3.exe 10892 QueryOpen D:\Program Files (x86)\Steam\steamapps\common\Arma 3\netstuff\netStuff.exe NAME NOT FOUND