Why do receivers have a choke but transmitters don't?
Why do receivers have an inductor specifically designated as a choke (RFC) in their circuits but transmitters don't?


Your assertion is incorrect.
Chokes / RFCs are used in transmitters and receivers when the designer thinks they are appropriate. Providing a single example of each does not make your point well.

The purpose of an "RFC" is to block the passage of RF energy but to allow DC or low frequency AC to pass essentially unimpeded. This will never be achieved perfectly but the (usually) large difference in frequency of audio and RF means that an unductor can have a large impedance at RF frequencies and minimal impedance for audio, and also have a low DC resistance so DC current causes minimal voltage drop.

Many transmitters use an RFC to feed DC to the "final" amplifier while blocking RF. 

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Example

Here is a classic "RF final stage with choke" diagram.
12 VDC is connected to the transistor collector via the RFC.
The RFC prevent RF "escaping" into the power supply.
This circuit is intended for 88-108 Mhz operation.
At say 80 Mhz the 1 uH RFC has an impedance of about 550 Ohms.
The following 0.1 uF capacitor on the 12V supply has an impedance of about 0.02 Ohms so the RF reaching the 12V supply is "divided" by a factor of about 0.02/550 = a factor of about 25000. (It's more complex than that, but that gives a guide. )



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