Coaxial S/PDIF input circuit
The logic gates have a "U" in their name, which stands for "unbuffered".

The SN74LVC1GU04 datasheet says:


  8.3.6 Unbuffered Logic
  
  A standard CMOS logic function typically consists of at least three stages: the input inverter, the logic function, and the output inverter. Some devices have multiple stages at the input or output for various reasons. An unbuffered CMOS logic function eliminates the extra input and output stages; the device only contains the required logic function which is directly driven from the inputs and directly drives the outputs.
  
  The unbuffered inverter is commonly used in oscillator circuits because it is less sensitive to parameter changes in the oscillator circuit due to having lower total gain than a buffered equivalent. To learn more about how to use an unbuffered inverter in an oscillator circuit, see Use of the CMOS Unbuffered Inverter in Oscillator Circuits.


In an oscillator circuit, or an S/PDIF input circuit, the input signal typically does not have logic voltage levels. The DC-blocking capacitor makes the circuit independent from whatever signal level the S/PDIF sender uses; the feedback resistor then biases  the inverter in its linear region, near the switching threshold.

You do not need a DC-blocking capacitor after the transformer only if the transformer's output signal is not suitable for the following circuit. This would be the case for a logic gate, which does not support negative voltages.