IMO, Regulus vs Rook is definitely one of the game's most slanted demigod matches. It's not unbeatable, but it's definitely Regulus at his best and Rook at his worst. However, there are some ways to deal with it.
As with TB, you want to keep your towers spread out so he has trouble hitting them all with one AoE ability. Regulus is a little easier to stop than TB in this regard, and you should be able to deal with his area of effect damage with some modest spacing. Your shoulder weapons are your friend here, since usually they will take a free shot on Regulus every time he tries to get a free shot on you. I'd probably avoid hammer slam agianst Regulus and do structural transfer instead. He can throw mines under you during its setup, and the end result will probably favour Regulus even if you get a direct hit with the hammer.
I find the key to playing Rook is to stop caring about other demigods, and this is especially true about Regulus. Your goal is to push, meaning you want to move your towers forward and whittle away the enemy tower lines. I've won plenty of games as Rook without ever getting a kill. Regulus can snipe out your towers, but until he's a very high level the ability will recharge faster than he can kill them. This means that if you play defensively your fortress will grow faster than he can blast it down. You can actually push quite nicely even with active resistance, which is where Rook shines.
The final thing I'd add is that if it's a 1v1 Rook is in very bad shape. He has trouble holding on to flags across the map and he's easily outflanked. If you're in a team game, all you need to do is hold Regulus off and keep up your push. Another demigod coming up from behind can easily kill Regulus if he's wasted all his mana trying to break down your fortress. Just tire him out and play the Rook as the fortress he is.
