That example would be fantastic to have another label on the left for the other time dimension.
For your example showing years, I'd think that other dimension would be months, such that the top slot would always be jan.
Another example would be if the main timespan was a day rather than a year, the other time dimension could be hours, such that there would be 24 slots available for each day for an image like you show.
I can see you don't stack vertically like that. Each event for a given year is just stacked to fill the space, but there would be more info if the spacing was by the months those events happened and you had to scroll vertically to see it all. The compact view supports that types of vertical scrolling.