The large IC is a PLL synthesizer used to generate the carrier frequency, most likely times 4. In a conventional design, this would be followed by a quadrature divider, usually realized as a two stage johnson divider feeding two balanced modulator stages, one for I and one for Q. The I stage has a dc bias applied to the modulating input to created the 1+L+R term. The other is left as a balanced modulator being fed L-R and pilot at its modulation input. The two signals are then summed, low pass filtered to allow the clipper to recover the carrier correctly, and then limited. This phase modulated term is used as the carrier drive for a stereo transmitter.
Any practical implementation also involves adjustable delay and equalization networks necessary to allow the exciter to precisely duplicate the amplitude and phase response of the transmitters modulator stage. Because real world transmitters have both group delay and amplitude roll off in the modulator, the response must be duplicated for the signals feeding the quadrature modulator or the stereo separation loop will never be closed, and poor separation will result.
It should also be noted that a precise demodulator is required to properly setup such a system, such as a modulation monitor modified to receive your transmit frequency, or with less precision, a stereo tuner with wide IF filters installed.
For the average joe, the linear amplification approach is a lot less involved and requires far less precision and hard to build/buy gear.
+-RH