First off you need to install 2 additional things before this application will run.

Grab ahold of winetricks

wget http://www.kegel.com/wine/winetricks

Then run the following

chmod +x winetricks && sh winetricks vb6run

This will install the visual basic 6 runtime, if you've already done this before for whatever reason, no need to do it again.

Next you'll have to install MSCOMCTL.OCX

Extract that and place the file in 

.wine/drive_c/windows/system32/

There the application will now start! Now onto the next problem..getting it to see your drive.

For this I used a 0800 flashed benq xbox 360 drive, I connected it to my computer and turned the comp on with the tray open, like you have to do in windows, although I'm pretty sure Linux is a lot better at recognizing it instantly, so you should be able to hotplug it just fine. (Edit Note: just tested hotpluging works fine, no need to restart comp to get it recognized)

*Note* For some reason I could not get Xbox Backup Creator to see my benq drive as long as I had my regular dvd drive plugged in, it would always see my regular dvd drive no matter what I set in winecfg. Its possible xbc just sees the first dvd drive in your satachipset, I had the regular dvd drive in sata2 and the benq in sata3. SO if you cant get it to see your ripping drive after following the below instructions, try unplugging your regular dvd drive.

Anyway...insert your game and wait for Linux to prompt you what to do with it. Select open in folder (get it mounted) strangely enough this mounted it to

/media/XBOX360

 for me, remember where yours is mounted to! 

Now open up wine configuration 

winecfg

 And go to the "Drives" tab you can add this under a new letter or you can use an existing one, although if you don't understand what each letter is there for..its probably a good idea to make a new one. So select F or whatever from the letter dialogue. Now find the Path entry box by default (if you choose to use a new letter) it will be set to just / in here you insert where Linux mounted your 360 game so for me it would be 

/media/XBOX360

Yours might be different! Once you've entered the path click "Show Advanced" and Type should be, by default, set to "autodetect" I found this is what was messing things up for me, so from the drop down-list select "CD-ROM" you can click Hide-Advanced now if you want. Then press Apply then Ok

*Also* a side note, I wanted to make it obvious that once you make this new letter you should re-use it everytime you want to create a backup if xbc fails to recognize your drive the next game you try and backup and you have to do this again. You don't want to keep adding pointless letters to the drives tab!

Now the golden moment! Fire up Xbox Backup Creator and it should recognize your drive and the media in it, just like it does in windows! You shouldn't have to change any of the default settings, just make sure "complete backup" is selected and press start! 

Once it is done ripping your iso, please be sure to check it with abgx360! That's another program entirely and out of the scope of this How-To, but there is a Linux version with a gui! Also to burn the iso I did not try using the built in burning feature, I used growisofs: tutorial on that here.

Enjoy! :)