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Besides some movement in the tiny individual cells, the black spots are not moving, not sure what the timelapse is trying to show. I looked for some 30 seconds, waiting for the bigger structures to start moving at all, before noticing that it seems to be looping every 3 seconds or so (not sure, the site lacks a seek bar or other duration indicator). Nothing happens that I can tell. What are we supposed to be seeing here?

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(For some more details, see also [1].) The bright boiling granules (comprising most of the image) show photosphere convection. There's also the inward movement of the tips of penumbral filaments (which surround the dark sunspot cores), though the material in them flows outwards ([2]). Note how granules get deformed in constrained areas before the two major sunspots.

All this can be seen in a "somewhat" higher resolution on time lapses from professional telescopes, e.g., [3] (from the 1 m diameter Swedish Solar Telescope).

[1] https://en.wikipedia.org/wiki/Sunspot

[2] https://en.wikipedia.org/wiki/Evershed_effect

[3] https://ttt.astro.su.se/isf/gallery/movies/2010/

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