How does the Infineon REAL3™ depth sensing imager chips measure time of flight for each pixel?
It uses a Photonic Mixer Device.

The REAL3 imager uses a sensor from pmd technologies(see the bottom of that page). PMD technologies is named for their use of Photonic Mixer Device technology.

As you speculated, it does use pulsed light. Specifically, it modulates the outgoing beam with an RF carrier and then measures the phase shift of the return signal. It is captured with a CMOS sensor.

If you want to dig deeper into how phase is captured from a CMOS pixel, PDM technologies only states that the CMOS is "coupled" with a DSP. But there are academic papers explaining the process such as this one (to be fair, this is from canesta, a competitor of PMD). One of the first questions that came to mind for me is how they would capture timing data, a typical CMOS is coupled with a shift register, and polling pixels by reading the rows would probably not be fast enough to capture an RF frequency. Even at the lowest RF frequency of 300 kHz, polling would require you to access each pixel in the GHz range to get any meaningful phase comparison data.

It turns out it modulates the gates for the pixel sensors in sync with the light, then it reads the voltage difference between the two nodes.

To quote the paper linked to above
"The differential structure accumulates photogenerated
charges in two collection nodes using two
modulated gates. The gate modulation signals are
synchronized with the light source, and hence
depending on the phase of incoming light, one node
collects more charges than the other. At the end of
integration, the voltage difference between the two
nodes is read out as a measure of the phase of the
reflected light. Thus, in effect, this pixel
simultaneously performs the function of mixing and
low pass filtering."

Finally here is the relevant patent.