Anton Moss

That's awesome, Umang_Raj beat me to it. I'll post my APEX version as promised. You have several options now. One thing worth noting with my setup is that it uses the Skin Controls feature, so you'll have to make sure it's enabled in your viewer state settings by pressing "p" in the viewport and making sure "Use Skin Controls" is checked:

Here's a kinefx example. I'll upload an APEX example later. Also, I dig the music track in your video.
So basically, I'm setting all the joints under a single root joint and all the other joints have their logic set up in a rigvop. It's not perfect, but the logic here is pretty simple; it's just a series of blended transforms. A similar concept can be applied using APEX.

Pretty late to this and for posterity, this is in the houdini docs for Rig Pose:

Enforce Transform Limits

When turned on, if your skeleton has any joints with defined rotation joint limits (as set up by the Configure Joints SOP node), then you will not be able to rotate those joints past their set limits when posing your skeleton with the Rig Pose handle in the Rig Pose viewport state. See Rotation limit handle viewport state visualizations for a demonstration of this behavior. You can also turn this option on/off per joint with the F hotkey.

You need 1 of the 2 nodes below before your rigpose:
configurejointlimits
configurejoints

Displayed in the viewport help, you can then hit F or shift + F to flip the limits

Example: