I try to format the output for you 
chris@chris-TECRA-A1 ~ $ mkdir -p "HOME/.wineprefixes"
chris@chris-TECRA-A1 ~ WINEPREFIX="HOME/.wineprefixes/eve/" winecfg
wine: created the configuration directory '/home/chris/.wineprefixes/eve'
fixme:storage:create_storagefile Storage share mode not implemented.
err:mscoree:LoadLibraryShim error reading registry key for installroot
err:mscoree:LoadLibraryShim error reading registry key for installroot
err:mscoree:LoadLibraryShim error reading registry key for installroot
err:mscoree:LoadLibraryShim error reading registry key for installroot
fixme:storage:create_storagefile Storage share mode not implemented.
err:winediag:SECUR32_initNTLMSP ntlm_auth was not found or is outdated. Make sure that ntlm_auth >= 3.0.25 is in your path. Usually, you can find it in the winbind package of your distribution.
fixme:iphlpapi:NotifyAddrChange (Handle 0x10ee8a0, overlapped 0x10ee8ac): stub
wine: configuration in '/home/chris/.wineprefixes/eve' has been updated.
chris@chris-TECRA-A1 ~ wget “https://binaries.eveonline.com/EveLauncher-1602194.exe” -O "HOME/.tmp/eveinstaller.exe"
chris@chris-TECRA-A1 ~ WINEPREFIX="$HOME/.wineprefixes/eve/" wine "$HOME/.tmp/eveinstaller"
/home/chris/.tmp/eveinstaller.exe: No such file or directory
He is missing a ‘$’ in the download command so wget can’t create the .tmp directory in $HOME.
Besides this why will you create a .tmp in $HOME only for tihis installation? Just let him download the installer in his browser and show wine the full path to the download.