Firstly, only valve (tube) amplifiers match the speaker impedance to the amplifier impedance - they can do this as they use an output transformer.
Transistor amplifiers work very differently, they have a very low output impedance, and feed into the (relatively high impedance - 8 ohm) of the speaker. The actual output impedance of a transistorised amplifier is usually in low fractions of an ohm, or down in the 10's of milliohms.
The reason for 8 ohm (getting back to the original question) is a question of power!. If you apply the formula W=(V*V)/R, you will see that for 20V output (RMS) an 8 ohm speaker will give 50W (400/8). If the speaker was 80 ohms, you would need 63V RMS for the same 50W.
For a valve amplifier, it doesn't matter much - you simply wind the secondary on the transformer so it matches. In fact, 16 ohm speakers were the most common back in those days.
With transistor amplifiers though, the output voltage governs the power, so by dropping the speaker impedance from 16 ohm to 8 ohm it doubled the available power for the same voltage output. Likewise for even more power, it's dropped to 4 ohm, particularly for in-car use, where you have a very limited voltage supply.
As for the 270 ohm and 100uF, it's making no effort to match anything, all it's for is to limit the load on the processor pin - the fact it wastes almost all the power doesn't really matter, you are only looking for low level beeping noises. As suggested, a simple transistor could be used to provide more power to the speaker, but I suspect you would probably find it a bit loud.