The way he phrases it, NATO was essentially at fault and the Russian response followed from that. I don't buy that he misspoke or we misheard; the line of reasoning was very clearly stated. We can quibble about what "taking sides" means, but the message he meant to convey was that the current outcome was the US's responsibility.
Chomsky's line of reasoning was clear, but it's always been very weak on this matter (he's said this quite often). It largely ignores the Kremlin's agency; it hardly matters what the US did here since the Kremlin had choices too and those mattered much more. Even more problematically, it ignored both Ukrainian and the wider post-Soviet region's agency as well. NATO expansion was never forced on anyone; to the contrary, it was eagerly sought after, and why? Because the Kremlin wasn't to be trusted, which turned out to be an accurate prediction.
It didn't have to be so; the Kremlin's institutional mistreatment of its neighborhood _caused_ that mistrust and sustain it to this day. The Kremlin could have acted in good faith, and would have continued to receive the warm welcome from western governments that the initial post-Soviet governments did. It could have mended the Soviet-derived mistrust in eastern Europe, and likely easily so given it's richness in natural resources, and the logistical centrality that attracted trade between former USSR nations via Russia, and it's initially warm reception by western powers.
The hint of far-future NATO membership was a "threat" to Putin the way mere talk of bolt-cutters are a threat to a kidnapper. That threat might well have been real, to be clear, but framing it the way Chomsky did isn't helpful; it obscures Putin's (or the Kremlin's inner circle's) choice to be an oppressive, almost colonial power ruling over it's neighbors.
The problem never was talk of bolt-cutters, the problem is that people _wanted_ those for a reason.