Does this article's appendix contain an error (is the heating system described integral control)?
Without looking at the paper, and responding only to your question- the heating system described is called proportional control in the industry (assuming the setpoint is temperature, the measured variable is temperature and the output is power-- as is typical). In fact in many heating systems the gain can be high enough that the droop due to demand changes is negligible (and the system can be correct either by changing the setpoint or by applying a correction factor called 'manual reset' that the error is nulled a given setpoint with nominal demand. 

So, you are correct that if there was a large demand change from nominal there would be a persistent error with proportional control, but it's not necessarily of any practical importance. 

The thermal capacity of the object being heated does indeed introduce a pole in the response, but the heat loss increases with temperature difference (at least proportionally, but often much faster with convection or radiation losses) so the result is not an integral control response. 

If you had a block of material that was sufficiently isolated from the environment (almost no conductive, convective or radiation losses) then you could consider it to be an integral controller, but that does not represent even a rough approximation to reality in any of the thousands of systems I've worked with.