I play rook with a somewhat different philosophy..
Tower I
Archers
Slam I
Tower II
Tower of Light
Boulder Roll I
Tower III
Trebuchet
Struct Transfer I or Slam II (depending on how much love i'm getting)
Tower IV
Levels 10+ i go for slam/roll or more struct transfer, depending on what i need more. Poisoned Arrows is absolutely mandatory if the game draws out until level 15.
Favor item of choice is the Heaven's Wrath - aka Ion Cannon.
The aim of this build is area denial. I pick a lane and that lane is mine.. If you want it, you better bring some friends as you alone will never be able to take it from me. Once the lane is clear of enemy towers, i usually move to a new one. The Ion Cannon allows me to farm creeps on virtually any point of the map.. some maps even contain chokes, where you can farm multiple spawns at once
This resuts in me levelling pretty damn fast compared to everyone else. (You obviously have to take your teammates into consideration and not kill creeps they would be farming otherwise) Also the item allows me to participate in many demigod kills ( or finish fleeing demigods ) and as such receive money from those as well.
How it plays out:
Early game you go and pick a lane.. The standard starting gear is Scaled Helm + Banded Armor. This usually gives you enough of an edge to - coupled with towers - scare any single demigod away. Once you have your lane, you start farming for gold and xp, using the HW favor item whenever the opportunity presents itself (whenever its not on CD). Once you reach level3, you become rather dangerous to any single demigod entering your lane. Even though your slam is unlikely to hit, if it does, your towers and archers can usually finish off the guy. Do not forget that you have an extra 250 hp damage at your disposal
I rather not count how many enemy demigods have died to that devilish favor item.
The first items i usually buy are Vlemish helm and Unbreakable boots. Some might argue that armor would be better, but the boots give more HP than armor would and also give me much needed mana. Lots of it. Also.. 2 teleport scrolls are mandatory along with a single lock. Next on the list are nimroth's chestguards. If im swimming in money and theres really nothing i could upgrade in the citadel, i sometimes upgrade my banded armor to to a groffling plate, but there usually always is something to upgrade and if not then im better off saving the gold for creep upgrade later.
Anyway, once the first few levels, the game settles into a pretty steady rythm. You hold the flag, you creep, you lay down towers, you try to kill single demigods, you evade / run if there are more than one of them coming for you. You need insane burst and plenty of stuns to remove a rook. That is, if he pulls back in time. If you manage to jump him, hes in trouble.
A good fallback tactic is to keep laying towers as you go, so that even if the enemy catches up with you, there will be some added firepower in range. Quite frankly.. i have yet to see demigods chase a rook with his towers built and get away with it.
Any rook using his head would have trebuchet picked at level 8
Why that? Well then.. it is built on top of their head isnt it?
That thing sometimes clears a lane without me even noticing
Its insane how easily it can take down towers, even ones that are well covered by fog of war.
Thats my tactic as a rook. I do not claim it to be the best one, but i believe its one of the better ones. Also.. this tactic is meant to be used in 3v3+. Less than 3 players would require a degree of mobility that the rook simply does not have. Maybe on a very small map like prison or crucible, this rook would be viable, but i prefer 3v3+ anyway.