A couple of thoughts on the dead FET:
Two major differences between the original flyback circuit and the one you posted are apparent. The frequency is (probably) quite different, and maybe more importantly, there is no flyback tuning capacitor across the primary.
In a basic flyback circuit, current in the inductor builds up as long as the transistor is on. The higher the power supply voltage, the faster the current builds up. When the transistor switches off (assuming instant turn-off and everything is ideal), the voltage on the drain will rise in an attempt to keep the current flowing as the magnetic field in the flyback transformer core collapses. This voltage can get to be very large. In TV sets, most of the energy that was stored in the magnetic field in the core is transferred to the flyback tuning capacitor after the transistor switches off, and then (in the "falling" half sine wave of the flyback pulse, is transferred back to the flyback transformer.
The maximum voltage on the drain is determined by the amount of energy stored in the core (related to the volt-seconds across the core during the time the transistor conducts and the inductance of the primary of the flyback transformer) and the size of the capacitor. The larger the capacitor, the lower the power supply voltage, or the shorter time the transistor was on, the lower the peak drain voltage (and also, the lower the output voltage). With no flyback capacitor, you have very little capacitance, so the voltage could easily exceed the breakdown voltage of the FET, thus dumping all of the energy stored in the flyback transformer's core into the FET. And it might only take one or two cycles to kill it (depending upon the amount of energy in each cycle, and the design of the FET).
By the way, the flyback transformer was probably designed to work best with one particular flyback pulse width, and even with monitor flyback transformers designed to operate independently of the deflection circuit, a high Q, low value inductor is put in parallel with the flyback transformer's primary. This allows high frequency operation (the inductance of the flyback primary is usually pretty high) and it has the added benefit of providing a lower tolerance resonating inductance, and therefor more accurate flyback timing that would otherwise be obtained.
One other thing that the flyback capacitor does is slow down the risetime of the voltage on the drain, giving the drain time to turn off so the peak power is not so high.
In case I did not make the point about frequency clearly: If the gate drive pulse is too wide, the drain current will be too high.