Such a ridiculous comment. There are many aspects of civ5 that are deeper (e.g., removal of that ridiculous research slider, just to get started), and others that are shallower. Same can be said for micromanagement (which does not equal "depth"): more in some parts, less in other. I guess there has been a general reduction in number of units, buildings and so on (if that's what you mean by "depth"). It's a whole new system and it still has some serious problems, I'll agree to that. But the whole "depth" argument seems very shallow to me.
The point is, "depth" to many means having a set of choices which typically interact with each other.
Picking one option confronts you with the costs of opportunity of not having picked another option.
In this context the infamous slider actually means something: adjusting it may give you more gold out of your total commerce, but inevitably less science (or espionage, or culture).
In Civ5, you can simulate this by re-allocating the workforce from a trading post to a specialist's slot in a library, but you have to do:
1) select the proper city
2) deselect the trading post
3) select the specialist's slot
4) re-adjust city's workforce (based on the governor's settings)
This is an example how Civ5 actually increased micro-management without any gain. For sure, in this area Civ5 is by no means "deeper" - it is just more tedious in terms of manual work.
An example for depth would be that in Civ4 you could chose whether you wanted to build a pasture, a farm, or a hamlet on a tile with cows. In the case of going for the pasture you would also want to have a road...
Another example would be the civics: Although you literally could play the whole game with the same settings, it was advantegous to adjust them according to changed circumstances from time to time. Nevertheless, it came by the costs of having anarchy.
Similar it is with the infamous SoD: moving your stack was significantly easier than moving 4 to 6 units one by one, but to keep your attack going you would want to fight the siege in an optimal way.
This means to check which unit(s) have to attack first. Based on the individual combat results, you would want to change the sequence, sometimes meaning to sacrifice a less important unit to gain an advantage for the next unit.
Combat was completely different in Civ4, but for sure not less demanding.
Bottom line: in total, Civ4 was by far the "deeper" game. You constantly had to make significant decisions to get next to optimal results.
In Civ5 you are just rolling along predefined tracks.