I could not open this game in the Mac system, it shows that EC 1.0.1 (mac) cannot open

Yeah it isn't a permissions issue, it simply says the file cannot be opened.  The executable bundle wasn't made correctly.  You have to open a terminal, navagate to "[download directory/Elven\ Conquest\ 1.0.3\ \(mac\).app/Contents/MacOS" and then do a "chmod +x Elven\ Conquest\ 1.0.3\ \(mac\)".  This means the developer never actually tested the mac version, which is frankly sad