Yes. I deal a lot with both breakers and fuses. As a general rule, the thermal portion of a thermal magnetic breaker will likely trip in under 3 hours with a continuous load of the nameplate rating, but may trip on a load as low as just over 80% of that. For a 40A breaker, that's 32A. FYI, with a 41A load, even a 50A breaker might trip with this heater without the breaker panel being in a relatively cold location. I can attest to returning home from a long day servicing a remote site, to find out at 2am that the 30A breaker tripped with a precisely 24A load, just so I could turn around and drive the 3 hours back to reset it and turn something off.
The magnetic portion usually doesn't come into play until 5x the nameplate rating.
Back to the OP's issue, this wasn't an overcurrent situation - YET. Let's think this through with ohms law. What you have here is a variable resistor that varies from 11.5 ohms (when the element is its full length; it looks like you have two elements in parallel, with each at 5000W to add up to 10kW) down to something closer to 0 ohms when it's completely burned up. By the time it burned to half it's length, that one element would be pulling 41A on its own. As it shortens, it will get hotter and hotter until at some point either it get so hot that the wire burns back faster than the arc can keep up (think flux core welding wire) and the element fails "open", or it gets so short that the current increases to the point that the breaker actually trips.
I'm sure the inadvertent arc welding show was quite dramatic, and the instructions do warn you to not store it near any flammable liquids or vapors, but your home wiring remained safely protected by your circuit breaker, and adjacent combustible surfaces were never exposed to dangerous temperatures (as can be seen by how much of the paint remains on the heater). So, I don't believe this was likely going to run away into becoming a house fire, as much as such a situation was a possibility.