While difficult to test I suspect that if we restricted chess players to the same age
and tenure profile of Arimaa players a machine would romp over the novice chess
players (max experience 13 years, average perhaps 7).
You're a decade too late. Even a modestly budgeted machine will (if not intentionally underpowered) romp over master chess players.
I get what you're saying and I'm sure an arimaa grandmaster, if one existed, could beat that particular program. However, you're ignoring the other side of the coin. There have been orders of magnitude more effort expended on writing chess-playing software vs. arimaa-playing software.
Now should I bother to learn the game at all?
Go is much simpler and deeper (although computers are getting pretty good there, too.)
Arimaa isn't a bad game, but despite the claims of its creator I'm not convinced it's simpler than chess. Chess has a few idiosyncratic and tournament-specific rules (three move repetition, castling, double pawn move and the rare en passant capture, having to "checkmate" the king instead of simply capturing him, etc.), but if you ignore those for a moment... chess has straightforward capture, a static setup, and a single method of winning the game. The only thing you have to actually memorize are the 6 different piece movements, the unique rule about knight movement, the unique rule about pawn movement, and the promotion of pawns bit. That's pretty much it. All of the other rules in chess are there for historical reasons or to improve the pace of gameplay among experts--they don't drastically affect the flavor, tactics or depth of the game. If armiaa became a worldwide pastime played by millions, they would surely develop their own array of minor rule tweaks.
So, compare chess's fundamentals (ignoring the ) these are arimaa's fundamentals:
1. Moving one piece one square (plus pushing/pulling--see below) counts as one move. You make four moves per turn. Not bad. It's only slightly more complicated than "move one piece per turn", yet being able to split up a single turn among multiple pieces or pool it all into a single piece is a great way to add depth. (It's not unlike action points in Fallout.) And other than rabbits the pieces all move the same way--obviously, this is simpler than chess.
2. Piece interaction and capture is, um, involved. First, you have a nested hierarchy of pieces that must be memorized (yes, it's "easy" because it's easy to remember that an elephant is bigger than a horse but I don't think that makes it simpler than chess's "any piece can capture any other piece".) Second, there are four different ways to influence an enemy piece: you can pin, pull, push or blockade (blockades only exist in chess in the special case of pawns.) This influence can be used to maneuver an enemy piece over a special trap square, which is which kills the piece... unless there's a friendly piece nearby to save it.
There's a sort of intuitive, real world justification for what is going on ("you see, the horse is grabbing onto the cat's tail, and these four squares here with stickers on them are actually deep holes..."), but I'm not sure how you can call the actual game mechanics simple as compared to chess.
3. The victory condition is getting a rabbit to the other side of the board or killing all of the opponent's rabbits. Like pawns, they can't move backwards. Let's just consider for a moment a game of chess wherein the goal of "kill the king" (again, we're ignoring all of this checkmate nonsense that grew over the centuries) was changed to "kill all of the opponent's pawns". That this would make the game deeper, I don't doubt... but simpler?