Space Empires 3, 4, 5 have exactly this. There are 3 resources: mineral, food, radioactives. Planets (and minable asteroids) provide variable quantities of each. Buildables cost various amounts of each. Normal races "spend" 95%+ mineral, but oddball races can tweak their ratios, e.g. races that have Organic components might spend 90%+ food instead.
It doesn't really change much. You still colonize everything you can, fill all bins as efficiently as you can, and build as fast as you can.
RBEs have the flaw that they stray backward to the barter economy, which means all desirable quantities in your life form a huuuuuge clique (complete graph) of directed exchange-rate arcs (arcs are not even symmetric). Then every transaction and interaction requires you and the other party to haggle peer-to-peer. Money is a convenient lingua franca, or the hub in a hub-and-spoke topology (or the server in a server-client architecture). Then you need only convert everything to and from money, which sure saves a bunch of people a bunch of work.
Ultimately, what you contribute to a society is your career-years of production. With this, you accumulate all goods for your existence, plus maybe amass a surplus (or incur a deficit). Bartering is a pretty inefficient way to manage all those transactions.
It gets (much) more complicated when we consider wealth creation. In our (admittedly low-tech, Earth-biased) world, your worth is not merely the sum of Lego brick things you churn out on an assembly line, but also encompasses some great new idea you invent, or a new iphone you assemble consisting of a bunch of stock parts in a novel configuation, or an entertainment you participate in that draws vast attention. What's really going on there? The RBE aliens currently observing Earth are equally perplexed when they see us going gaga over Apple/Samsung/Google's latest gizmo. To them, the resources haven't changed, they've just been packaged differently. But to us, on an Earth-societal level, there is apparently an uber-quantity that we can roughly call collective human interest, and it is malleable: human consciousness produces finite quantities of it, and it gets distributed at human whim across every conceivable thing in the world. Then value or worth is a consensus achieved by (insert cosmic punch-line here) something akin to Google's PageRank algorithm. If 2 billion humans suddenly think it has value, then poof, it does. If they lose confidence in Radio Shack, it falls, even though its tangible resources haven't changed. Interest creates demand, demand creates value.
And I think this will always be true, so long as consciousness exists(!!). Even when we cross the mythical sociological threshold of eliminating scarcity, I think there must still be some way to measure collective interest, and correlate that to value. RBEs don't, by themselves, resolve conflicts among alternatives. For example, a forest has value as a forest, or as timber, or you can clear-cut it for the arable soil, or strip-mine it for stuff a bit further down ... or sink it and grow radioactive kelp. So it could provide several different resources, but only one at a time, and your choice tends to be permanent. That decision can't be made at the resource level alone. And even if you do have the resources and factories, there are choices of what to build. Something other than resources must exist to drive those choices.
In fact, maybe RBEs simply don't go far enough. They're correct that money shall vanish, but they're wrong that resources would take their place. Gilmoy's counter-claim: It's not resources, but conscious interest. If you're interested in building ringworlds, then those two gas giants become part of your resources. If you're not, they aren't. Resources aren't the bottom line; interest will drive you to find new resources. We do that today when we frack. Niven's Pak do that with the rest of the solar system.
I rather enjoy GC3's use of wealth because it drags in economic concepts and terminology, which is a literal gold mine for running gags and in-jokes. They're funny because they're familiar. (It would be even more hilarious if Drengin wealth suffers from workers who play games when they should be working -- we all whistle innocently and claim not to understand) As a game mechanism, wealth gives flexibility because it's totally different from mp and rp.
Perhaps when GC3 matures, we can already roll our own RBEs by modding a custom race.
- Tweak its tech tree and buildables to de-emphasize or eliminate wealth as a consideration. They don't produce it, they don't suffer its ills (add Approval mods to compensate), nor benefit from its abilities (can't rush queues, no black(hole) market).
- Flaw: GC3's UI has wealth deeply-woven into it, e.g. 1/3 of the wheel, 1/3 of the Planet Manage columns, rush builds, etc. So a wealth-less race deliberately eviscerates a fraction of the UI, which is an asymmetry you can't just mod away ...
- ... unless we can. If modding is sufficiently expressive, we might replace wealth with a completely different concept, which is a drop-in replacement for all wealth UI, but has different effects. For example:
- Asimov Terminus Atomics, and you produce atom-piety instead of bc.
- Asimov Gaia Allthink, producing harmony -- which Gaia really did use as a societal replacement for money.
- Flaw: if it quacks like bc, then it can probably rush-build and trade like bc ... which defeats the purpose, if the goal is to make this race really different from other races. So we'd also want the modding-facility to be rich enough that we could define moats between disparate quantities, e.g. to say "this is not wealth, don't equate it to wealth". A simple Boolean-flag would suffice

RBEs are a neat thought-experiment, but they've been done in 4X, and they don't really stand out. GC3 surely has bigger issues to grapple with. Anyways, I think it's too late at this stage to rip wealth out of GC3's engine + UI.