The antenna is matched to be 50 ohm at A (Fig. a). So, to measure it in practice, the author designed a 50-ohm transmission line which connects A to B. Am I right?
The antenna by itself is not a 50 ohm, resonant antenna. It will likely have a complex impedance that needs to be transformed to a 50 ohm purely resistive impedance (typically). That is the job of the matching network. I believe you can see the matching network in picture B just above the highlight box you added.
From the matching network, the designer has used a transmission line known as a GCPW (Grounded Coplanar Waveguide). Like any transmission line, the goal is to conduct RF current from point A to point B without radiating any RF energy while minimizing losses (attenuation). In this case, the GCPW has likely been designed to have a ZO of 50 ohms.
In the ideal case, the output impedance of the transmitter or receiver is specified as 50 ohms impedance and the antenna impedance has been transformed to a 50 ohm impedance. This minimizes the losses along the 50 ohm transmission line and allows the specified power to be conducted between the two points with minuscule radiation from the GCPW.
I think the input impedance and the performance of that antenna, if measured again at A, must be changed compared to those of the antenna only in Fig. b and c. That kind of antenna is significantly dependent on the ground plane. So, how can we know, when designing an antenna, an antenna will perform better or worse with integrated components like Fig. d?
The primary difference between picture B and D is that the transmitter/receiver components have been added to the board. These components are independent of the monopole portion of the antenna. The transmitter/receiver could also have been placed on another PCB (printed circuit board) but then some interconnect scheme would need to be used. This likely would reduce the reliability and increase the cost of the assembly but it may be necessary in some situations in order to meet form factor requirements.
Regarding the ground plane on the circuit board, this will inevitably form part of the antenna. A monopole antenna needs a return path for current. If a return path is not specifically provided, such as the second element in a dipole for example, the RF will find a return path through other means. In the case of this meander antenna, the ground plane on the circuit board becomes part of the antenna and thus radiates. This can be a design challenge because RF current is now flowing through the copper ground plane on the board and this can easily couple to other circuit elements. The designer needs to take care that this effect is understood through simulation and controlled in the implementation through careful attention to current path details.