Chrome doesn't start in Windows 8, gives an error message "Class not registered"

This seems to be an artifact of this bug, and seems to be caused by a system-wide install, as your screenshot indicates(Chrome is present in Program Files\Google\Chrome as opposed to %localappdata%\Google\Chrome)

Try checking for presence of these registry entries in HKEY_LOCAL_MACHINE (HKLM) & HKEY_CURRENT_USER(HKCU)and delete them:

HKEY_CLASSES_ROOT\Chrome  
HKLM\Software\Classes\Chrome (all of it)
HKCU\Software\Classes\Chrome (all of it)
HKLM\Software\Classes\ChromeHTML\open\command\DelegateExecute
HKCU\Software\Classes\ChromeHTML\open\command\DelegateExecute

1. Run cmd.exe in administrative mode ( search cmd.exe and right click, run as admin... )

2. Copy and Paste these each line, one by one in cmd and press enter. Cmd.exe will ask you Do you want to continue? Press "Y" letter and press enter...

REG DELETE HKEY_CLASSES_ROOT\Chrome
REG DELETE HKLM\Software\Classes\Chrome
REG DELETE HKCU\Software\Classes\Chrome
REG DELETE HKLM\Software\Classes\ChromeHTML\open\command\DelegateExecute
REG DELETE HKCU\Software\Classes\ChromeHTML\open\command\DelegateExecute

Here is the screen shot;

Note: Don't mind if cmd.exe print "ERROR: No path found" etc. Just continue to copy & paste and run each line...

Caution - These commands may delete your Chrome plugin ( add-on ) settings...

Create this reg file and double click on it to import it

Windows Registry Editor Version 5.00

[HKEY_CLASSES_ROOT\ChromiumHTM\shell\open\command]  
"DelegateExecute"=-

[HKEY_CLASSES_ROOT\Chromium\.exe\shell\open\command] 
"DelegateExecute"=-

[HKEY_CLASSES_ROOT\Chromium\.exe\shell\opennewwindow\command] 
"DelegateExecute"=-

[HKEY_CLASSES_ROOT\Chrome\.exe\shell\open\command]  
"DelegateExecute"=-

[HKEY_CLASSES_ROOT\Chrome\.exe\shell\opennewwindow\command] 
"DelegateExecute"=-

[HKEY_CLASSES_ROOT\ChromiumHTM\shell\open\command]  
"DelegateExecute"=-