At the end of the day Vonnegut was a liberal not a leftist. A lot of that philosophy is more or less "I agree with protestors of the past but the current thing is 'complex." See democrats on gay rights, trans rights, anti-racist movements, etc. Chicago, perhaps historically the most liberal city, is deeply racially segregated by design. Remember 'liberal' California voted against gay marriage. Obama ran as an anti-gay marrige candidate in 2008. The dems today have hypocritical views on trans rights, migrants, the I-P conflict, etc.
Vonnegut is a good everyday liberal (which is a big part of his commercial appeal imho, never overly challenging and fit in with the neolib NYTimes-style intelligentsia of the time) and good, if not great, writer, but people expecting him to be more to the left than that are just going to be disappointed.
I'd even argue this game is a great example of liberal idealism. That is to say the problem is sort of distilled down and punched down to individuals (hey this game should be taught to soldiers) instead of punching up the dynamics that actually cause the suffering of war he's trying to address (capitalism, MIC, white supremacy, oil politics, racism, colonialism, xenophobia, etc). Or at least it leans far more towards the former than the latter. I think "war is sad and bad" is a far more marketable and acceptable view to liberal readers than "hey we will need to fundamentally revisit and reform or even replace things like capitalism, the modern world order, and even things you might personally benefit from if we want a peaceful world." These types of writers play up to middle-class moralism and liberalism, which is a big market, but never challenge it too much.
Vonnegut wasn't a Chomsky or a Marx. He was an Anderson Cooper or an Obama or a Chris Christy.