Microtubules play a key role in cellular structure and function. Wikipedia explains it much more succinctly than I can. The takeaways are that microtubules give many cells structure, proteins bind to microtubules, microtubules are used to transport intracellularly, and that they play an important role in mitosis.

I would also point out that they are typically dynamic in cells, in that the growing end is capped, cut, extended, etc. which is critical to the information storage function that article describes (and would be permanent, it seems). So they would essentially encode a 'state' that could be reproduced. Very interesting article, good find.