For the record, I think Shaq would score 30+ points per game in today's league with great efficiency, but he would also be a problem for his team defensively because of his lack of defensive mobility outside of the paint.
I think anytime you're comparing players from different eras it's a fool's errand because there are just too many variables. The game has changed a lot since 2010, let alone since 2006 when Shaq was at the tail end of his prime. It's too simplistic to say "Well, Shaq dominated interior defenders in his time and interior defenders have only gotten smaller since then." There's a reason defenders are lighter and quicker now, and many of the factors that have caused that shift would be to Shaq's detriment.
Realistically, if Shaq came into today's league he would probably end up developing an outside jumper and also have some guard skills.
Michael Jordan, similarly, would probably be a 45% three point shooter and would have a killer step-back three.
I think Prime Shaq is more mobile than a lot of the starting centers in the league. Steven Adams, Horford/Baynes, Brook Lopez, and Marc Gasol are all starters on top-6 defense’s. None are particularly fleet of foot. An athletic Shaq would fit in just fine defensively I think, while maintaining his offensive dominance.
I think you're underselling Adams and Horford here a bit in terms of quickness / agility.
Besides that, defending the perimeter is not just a matter of raw physical attributes. Shaq had no experience defending perimeter players. I think it's a bit of a leap to assume he'd able to play modern defense without any problems adjusting to modern pick and roll play, the prevalence of shooting bigs, switch-everything defensive schemes, etc.
And of course there's the fact that in the latter half of his career Shaq often declined to play much defense, even though he wasn't expected to venture far from the basket.
As I mentioned before, we can assume that Shaq would have different skills if he were playing in the modern game, but I don't think that's the point of the original question.
Anyway, I'm sure Shaq would be great in any era, especially if he were acclimated to the mode of play of that era.
But I think it's silly to assume that he would be ultra-dominant in the modern league because there aren't as many big lumbering centers to check him in the post in today's league. There are a lot of reasons for that overall shift. One of them is that Prime Shaq is no longer in the league.