2 rooks and a queen are pretty much equal. At 1500-1600 games can't be perfectly played. Not yours, and as someone around the same rank, not mine. I'm sure their are better moves, and black did not really coorperate his queen and bishop as well has you did your two rook and bishop. He had no need for those pawn moves there either. I briefly looked, it could have drawn relatively easily. I wouldn't call it a difference in chess pieces' strength, just simply a difference in player's skill.
The power of 2 Rooks against a queen

yes, it depends on the position. with plenty of open files and ranks two rooks are definitely better.
what you have asked is, GENERALLY, right? i would say 2 rooks.
reason 1: 10 versus 9 points
reason 2: queen plays the role of many attackers, but one defensive unit. it cant defend 2 pieces at a time if opponent is attacking both pieces. besides, queen as the most powerful piece is a rather bad defender esp if opponent has two attackers vs the queen. sad case.
reason3: two rooks, when facing each other, is very, very strong. always double your rooks. two rooks means backing each other up, and they are togetehr 2 defensive units and a pretty pro attacking force too. queen has only itself. 2 rooks has backup for each other.
(: chew on it. food for thought.

so Waffl3sWaffl3s at move 64 what better would you have done in this position note that evaluation at this pint is (1.88), any wrong play would bring it to (3.09)

White didn't do anything but shuffle around. From move 30 to 60 almost nothing changes, then black gives away a few pawns and a bishop and the game ends.

I'll estimate the endgame started before move 22. I'm just going to analyze move 22 though. We see that white has a better pawn structure while black has 2 isolated pawns. Sure one is a pass pawn, but it is hard to protect. White simply had a better position and did not screw up. Black made a few minor blunders that cost him the game later on. As shell knight said, white only shuffled around. White did not really do much on move 30 to 60, meaning black is the cause for the blundered defeat most likely.

Also, a queen is worth roughly that of two rooks. However, there are no half points. I'd actually value each rook at 4.5. It's just my opinion however. Many masters and others have come to accept that two rooks is equal to a queen, at least those whose works I have read or talked to.
A good way to determine the relative strength of pieces is by having a chess engine play itself using various combinations of pieces. I usually do it by setting up the default starting position, leaving all the pawns in place for both white and black, and then deleting the rest of the pieces which won't be used in the comparison.
Whenever I've done this with 1 queen + 8 pawns vs. 2 rooks + 8 pawns, it is always a draw. It is also always a draw when it is just 1 queen vs. 2 rooks (no pawns), but I prefer doing the tests with a full complement of pawns, because it gives each side a basic line of defense and allows them to develop a position, rather than just immediately going into perpetual checks. Also, sometimes having a little bit more power would be enough to force a pawn promotion, but not enough to win if there were no pawns on the board, so including pawns in the test can reveal that.
As a side note, with no pawns on the board, 9 knights utterly trounce 3 queens; easily winning with up to 6 knights to spare. 3 queens can only handle up to 6 knights, 7 knights are too much.

There's one line in the Dragon where white gives up a Queen for 2 rooks and a pawn.
These material imbalances usually favor the player with the 2 rooks, but then again we have to take into account the static and dynamics of the position. For example in the aforementioned example, Black's superior development and active pieces usually outperform White's forces. Furthermore, Black's threats are usually too much that White has to give up an exchange.
Ohh, this exact variation was played in one of Chess.com's Team vote matches, I believe it was Hufflepuff vs. Ravenclaw or something like that. Anywho, this variation usually tends to favor black so that's why many people play 14. Qc5 instead of taking the rook.
Now, That's just speaking for this position. It's impossible to evaluate in general which side is better, but the side that has more active play will usually compensate more for the imbalance.
this one reminds me of how powerfuls rooks are against queen an a open board