Symptoms
The installation for the 4.6.8 Blackpearl and K2 for SharePoint 2013 1.0.1 client tools fails with errors on a 32-bit machine, whereas loading the same client tools on a 64-bit server with the same installation media works.
Diagnoses
This is related to the fact the client is a 32-bit instead of 64-bit.
Resolution
There are two bugs that have been logged and fixes are available for installing K2 Blackpearl 4.6.8 and K2 for SharePoint 2013 1.0.1 on a 32-bit client machine:
Bug 500207: Installer - K2 for Visual Studio 2010/2012/2013 - installation fails on a 32bit (x32) machine
Bug 540264: K2 for SP2013 Client components installation fail on X32 Machine
Contact K2 Support to get copies of these fixes.