Zig-zags in PCB traces can be for impedance matching, but also for control of signal integrity and timing.
In the case of antennas, impedance matching and minimizing reflection are the main reasons. Depending on the frequency and physical size of the PCB, a designer may include the antenna as a trace that is a single bar, a "L" or "T" shape, a loop, or a zig-zag. The goal is to match the length of the trace to the frequency in such a way that avoids reflecting power back to the circuit but also corresponds to a common denominator of the wavelength.
Bluetooth operates at 2.4GHz, which has a wavelength of ~125mm. Antennas are often 1/2 or 1/4 the wavelength, so you might find that the zig-zag trace is somewhere close to 31.25mm if "stretched" out.
The BTM-331 doesn't show an obvious antenna in the image, but might have one on the reverse side of the PCB or even included inside an ultra compact ceramic chip antenna like this WRL-00144.
Per the addition of the photo of the back side of the BTM-331, it clearly lacks a PCB trace-based antenna. Either it has a pin to connect an external antenna, as Dzarda suggests, or it uses an antenna that is very small.
If it uses an ultra compact antenna, its performance/range won't be very good. If it allows for an external antenna, then performance could be much better. The question then is whether you are comfortable buying or creating an appropriate antenna, and what sort of performance is acceptable.