The platform you read was probably written by the Economy Committee of the Green Party in question, which means whomever showed up when the Economy Committee held its platform-writing meeting.
It seems to me that the folks who showed up in your country were simplemindedly trying to be all things to all people. There aren't many Greens who are all that good at economics, as well. The main inspiration for joining the Green Party is the realization that the world can't go on forever the way it's been going. What do you think? Do you think capitalism can despoil the planet indefinitely the way it's been happening so far?
I'd be surprised if most Green candidates or Green voters agree with every word, or even most of the words, in all the platforms. I certainly don't, and I've worked on three campaigns for a Green candidate who basically holds your positions on the important stuff. So I think it's a long leap from a brief criticism of a particular Green platform to any broad generalization about the opinion of "all Greens" on political economy. My business has occasionally been to meddle with the education platforms, but I haven't found time for much else, especially since Green statewide meetings are often held in other parts of the state, far away from where I live.
At any rate, out there in England you have your own, competing, political party to promote. I'm not going to debate you about that. So whatever. Frankly, talk of "class struggle" in the US is cause for many to engage a good old-fashioned witch hunt, while the "communists" and "socialists" here in the States are split into about a dozen different parties with about 150 members each, most of them in Berkeley CA, Madison WI, New York City, Chicago, and Los Angeles. Ask Stuart Gort (or maybe DonS) about it; I'm sure he'll show you some good old-fashioned McCarthyist spirit.
I personally don't think that running candidates is going to do a whole lot, given corporate control of the election processes, and I don't think that having allies in public office is as meaningful as gaining any degree of power over one's life against global corporate control.
Sure, it would be nice if we could all hold our hands and proclaim socialism at once, but I don't see any harm in building communal and cooperative institutions now. After all, somebody's got to practice.