They record calcium activity in neurons. Calcium is a marker of neuronal activity (although the dynamics are slower than electrical ones). Calcium recording in the nematode is difficult, because the neurons are small, and the spread of calcium is very broad. The method is impressive and a great breakthrough. However...
1. A brain is a center of the nervous system. It's not strictly correct to speak of brains of nematodes. They don't have this separation of their nervous system. In the article they write of the anterior nervous system of the nematode, and say that their technique could be applied to brains of other animals. 2. The short clip is not a recording of all neurons. It's 70% of the neurons contained in the head ganglia.
Some people here speak of the mapping of the network. This was already done in 1986. The nematode is highly stereotypic. It's known what neurons there are (they all have acronyms), how many, and what they are connected to. The weight of these connections is not clear yet however. What is not clear are the associated neurotransmitters to these synapses and the strength of synapses. This determines how strongly neurons modulate each other and if the modulation is excitatory or inhibitory.
With some caveats in place, the potential of the recordings based on this technique is to help to get to the connection strengths, and to a functional connection diagram that then can potentially be used for predicting the animals behavior.