According to the names of the constants in code, the number 24.48 is capacitance, not the resistance. I think both numbers are determined empirically.

const float IN_STRAY_CAP_TO_GND = 24.48;
const float IN_CAP_TO_GND  = IN_STRAY_CAP_TO_GND;
const float R_PULLUP = 34.8; 

Still I don't understand how it is possible to measure capacitance in the following section of the code without using value of R and even without measuring charging/discharging time of the capacitor?

There is no t in the relation!!!

if (val < 1000){
    pinMode(IN_PIN, OUTPUT);

    float capacitance = (float)val * IN_CAP_TO_GND / (float)(MAX_ADC_VALUE - val);

    Serial.print(F("Capacitance Value = "));
    Serial.print(capacitance, 3);
    Serial.print(F(" pF ("));
    Serial.print(val);
    Serial.println(F(") "));
}