Do we classify vehicles by their propulsion systems? Or do we classify them by the energy they consume?
Is a hydrogen car a hydrogen car or an electric car? Is a compressed air car a compressed air car, or a pneumatic motor car? Is a diesel car a diesel car or an ICE car?
If you accept that we classify vehicles based on the energy they consume, it would be entirely reasonable to factor in the heating energy.
I think what JRP3 is trying to refer to is SAE's definition of hybrid (see page 5 of linked pdf):
"A vehicle with two or more energy storage systems both of which must provide propulsion power – either together or independently."
So we classify vehicles generally not by their "propulsion systems", but rather by their energy storage systems that "provide propulsion power".
An example is that even though a battery runs a gasoline/diesel/ICE car's accessories (radio, fans, etc), we can't call it a hybrid because of that. The energy storage system being examined has to power propulsion. So under this definition, an EV using parafin/ethanol based heaters would not qualify as a hybrid.
The exception to this classification is "EV" when used with modifiers (without modifiers, EV generally is a contraction for "electric car"). For example, the "EV" in HEV refers to "electric drive vehicle" not the energy storage (so any vehicle with electric motors for propulsion would qualify even if they had no direct electricity storage).
http://media.gm.com/content/dam/Media/microsites/product/volt/docs/paper.pdf
Since I gave that link, we might as well look at SAE's definition of PHEV:
"A hybrid vehicle with the ability to store and use off-board electrical energy in the RESS (rechargeable energy storage system)."
From the same document, GM's definition of EREV (which SAE has not recognized, that term was invented by GM):
"A vehicle that functions as a full-performance battery electric vehicle when energy is available from an onboard RESS and having an auxiliary energy supply that is only engaged when the RESS energy is not available."
First thing to note is that hybrid > PHEV > EREV (where > means "is a superset of").
So by GM's definition, a Pip is not an EREV, Karma also not an EREV (doesn't get full performance in Stealth mode). A weird effect of this definition is that if Fisker disabled the ability to select Sport mode (so it gets the same performance with ICE on, even if it's lower than the max they can get), then it would qualify as a EREV. And the other change Fisker can make is to add a bigger battery (so it is matched to the motor power so the ICE is not needed for peak performance) and it would also be an EREV.