If it takes you 1 second per visiting a single star (including the travel time), it would take you cca. 3 years to visit all the stars in some of the smallest galaxyies in the real universe as modern astronomy knows it. As for a typical galaxy, it would take you cca. 30 000 years, and for the largest known galaxyies cca. 30 000 000 years.
(given that galaxyies have 10^7 ~ 10^14 stars each, and cca. 10^11 stars in a typical galaxy such as our Milky Way; and also given that a year still lasts 365.25*24*60*60 seconds after such a long period)
(I recently passed "Astronomy and Astrology" with 4/5:)
As for the informatic aspect of the game, I think such things could be relatively easily generated in real-time as needed. And if you use a fixed random seed and a good random-generating algorithm that would depend mostly up to the coordinates (i.e. not up to the sequence in which things are generated/visited) you could have an infinitely large universe with relatively small amount of effort put into building it AND have it look the same to all players.
In short, I like it.
P.S.: the second video shows what? Stars? In which case they are waaaaay to densely packed.
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but maybe later.