Powering 100W amplifier with 12V rails from ATX power supply
You need to rethink your calculations.

Let's assume that the amplifier you're using has negligible losses. Then the very greatest power you can provide to the speaker is (12 volts x 12 volts / 8 ohms), or 18 watts. Music, though, is essentially sinusoidal, so the maximum sustained AC power, technically called RMS power, is 0.707 times the peak power. This means that your amplifier can only produce 12 watts. Note that the data sheet you linked to suggests a 22 volt power supply. Checking this against the previous calculation gives (22 x 22 / 8) x .707, or 43 watts RMS. And using the absolute maximum of 24 volts gives 51 watts. Close enough.

So the peak current will be 12 / 8, or 1.5 amps per channel, for a total current of 3 amps, and a total power supply requirement of 36 watts.

So, to answer your question, the unit does not pose a fire hazard. It doesn't provide nearly as much power as you thought it would, but that's a different question.