So I was having the same problem and found a workable solution.
Make sure all previous launchers for chrome are removed
Open chrome
Right click Icon only task manager and select Icon-Only Task Manager Settings
Select Launcher Matching Rules from the left pane
Click Add button on the right
On new dialog box click Detect Window Properties
Mouse pointer should turn to target, click on chrome window, this should auto fill some stuff
In same dialog next to launcher section click the file folder icon, Select launcher application window should open
Internet -> Web Browser -> Google Chrome
Click Ok -> Ok -> Apply
Now When you select show launcher when not running it should add the proper icon
If you right click on the launcher while chrom is running you will see a chrome item in the drop down menu, not sure how to remove this but it is only a minor annoyance. If you figure out how to remove this let me know. If you have trouble following I can probably post screenshots, let me know.
I have some screenshots but just realized they need to be hosted, I cannot directly insert them here. I forgot to mention that I copied the google-chrome.desktop file from /opt/google/chrome/ to my desktop and initially launched it with that prior to step 1. If you pm me with your email I can send you the pics, unless you can recomend an image host to use for these boards, I got about 12 screenshots.
Launch chrome from the normal menu > Right click the task manager box running in the panel SUSE Paste
Close chrome and launch from the new quick launch icon
This is exactly the same thing I have setup, my main task manager is at the top of my screen. My directions setup a quick launcher using the method in your paste however there are a few steps to do first for it to work properly.
I also could not find the Icon-Only item but there is a simpler workaround for this. Just open a terminal and run google-chrome then select ‘Show a launcher when not running’ for this one.
The problem with the initial one is that it does not call google-chrome simply.