Increase the range of RC controller
The way it is described in the OP's circuit quotation will probably mean it doesn't work because the transistor emitter is connected only to the antenna and there is no mention of a pull-down resistor to properly bias the added transistor.

I'll also say this about the quote. The person writing it has no idea what he is doing or why it works:


The existing amplifier only runs at 0.2V - if this is true then it won't be enough to bias the extra transistor stage.
Coming up with a statement of "it'll be a 15x gain" is not based on sound reasoning.
The author also says "It can be noisy as hell and it'll still get the message across". This indicates to me that he doesn't understand much about radios.


Increasing the power output from the transmitter, as previously said in comments, is probably breaking laws on transmission levels especially if the power (or voltage?) is increased 15 times.

More likely to get a good increase in range (maybe double) is to improve the radio receiver in the car - this won't be illegal.