The test results you have selected are very old and may not represent the current state of Wine.
Selected Test Results (selected in 'Test Results' table below)
What works
Bible, Bible font size Strongs tool tips Dictionary Bible search, accept, navigate Switching between full screen Bible, Dictionary, Commentary, and hybrid screen
What does not
Installers for downloaded add-ons. Workaround: copy the .bbl, .com, .dct files (etc) from the e-Sword directory on a Windows machine into ~/.wine/c/Program Files/e-Sword/
What was not tested
Graphics
Step viewer
Scripture memory
Additional Comments
*** I removed the wine version that came on this Fedora Core 1 machine.
(rpm -e wine) Then I downloaded the source code for wine 0.9.23 from winehq.org and compiled it:
make depend && make
(wait an hour)
(login as root)
make install
I think this will work under almost any reasonable linux desktop distribution.