Portable Generator Grounding
Grounding isn't the problem, your neutral is

Since the EZ-Generator-Switch for your furnace has a continuous neutral and ground, I'd recommend doing nothing additional here for grounding.  Your generator is already grounded through the ground connection from your house wiring to the EZ-Generator-Switch and the ground wire in the cord from the EZ-Generator-Switch to the generator.

Now, the neutral is a different problem.  Portable generators bond the neutral to the ground themselves as they're intended to be used as standalone supply sources.  Your house wiring also bonds the neutral to the ground at the main panel.  So, not switching the neutral to your furnace between your house wiring and your generator effectively parallels the two neutral/ground bonds, which is problematic from a Code compliance/safety standpoint (a GFCI equipped generator will trip its GFCI under these circumstances, and it can have other baleful effects as well such as inadvertently energizing grounded metal objects with circulating currents).

If you wish to use this generator only for powering your important things in this (hacky, but safe) way, you can remove the neutral/ground bond wire from the generator and set it aside.  However, if you do this, you'll need to replace the neutral/ground bond if you wish to use the generator for anything else.  A better solution would be to switch out your existing EZ-Generator-Switch for the version with the switched neutral -- that way, the two neutral/ground bonds (your house's and the generator's) never get put in parallel.