You could plausibly argue that if the Qin didn't do it, some other state eventually would. That's pretty much the prevailing view in elementary Chinese history, anyway - advances in state power, economic development and philosophical legitimation helped draw the various states closer towards each other (coupled up with the typical 'the people desired a union of China' and all that BS).
I think Chu's a capable contender for alternate unification - certainly it was the most powerful state after the Qin during the late Warring States period. A Chu union would be quite different from a Qin union, however, considering difference in language, culture, and the fact that the Chu political system was much more 'elite-consensus' than the autocratic Qin.
But let's say that China never gets united. I don't see Han or Wei surviving long-term... but the others have a decent shot at maintaining a stable-ish state system. You'd definitely see increasing divergence between the individual states, which had their own writing and language by the late Warring States. Inter-state competition would fuel advances in the military, naval, philosophical and political realms, while at the same time retarding a lot of the economic and social development that only a massive unified empire can really engender. At some point, the cultural differences between the states grows so large that a pre-industrial unification of China becomes impossible.
You'd probably still see the expansion of 'Chinese' borders, as individual states expand outwards in order to find more resources to compete. We'd probably see a late emergence of the Silk Road, as the pressures of war mean that luxury production is suppressed.
As time goes on, we'd probably see non-Han nations get drawn into/integrated within the East Asian political system (much like the German/Norse states were eventually integrated into the European system), Sinicization remaining a plausible possibility. It's not easy to say what Europeans will find in such a scenario (it's entirely possible that a fragmented China will collapse more easily to various horde invasions), but we can assume that Europeans will find a region that is more militarily advanced, more 'innovative' (in a political and philosophical sense), but less prosperous or socially developed than OTL.
IMHO, this would have some pretty big implications in its own right, especially if the first Chu "Emperor" doesn't rule as a Legalist in the mold of OTL's Shih Huang Ti (
e.g.).
Legalism was pretty entrenched by the times of the late Warring States - imho the Legalists had, pretty successfully, linked their platform to 'national strength', especially after the practical successes of Xin Buhai and especially Shang Yang's reforms. Chu's political system is of course not the Qin's (being much less autocratic), but I suspect the Legalist ethos will remain.