Meta AI hasn't actually done anything vastly different from what creators of the current wave of AI still image generators have done. It's used the same diffusion technique, through which the AI model buildings images by denoising virtual static to move toward the desired prompt.
It's only trained the model on captions for still images too, Meta AI says, “a model that has only seen text describing images is surprisingly effective at generating short videos.” However, it also gave the model unsupervised training on unlabeled video content so that it knows what sequential video frames look like – apparently it wasn't necessary to specifically train it to know how to combine them.