Defining Mao's takeover as inevitable may be a bit extreme in this case but Mao did have a few time-wise and setting-wise advantages during his consolidation of power over Chiang. Like the case observed back in the Weimer Republic and the Nazi Germany, the public tend to rely on much more extreme measures and leaders if the situation is desperate enough. This is probably why the Nazi Germany gained so much support from the crowd despite his monstrous behaviors afterwards.
Nothing in human history is inevitable, but it is not surprising. Mao had a great deal more support among the people because he was not as oppressive as the KMT was. He had his people treat the peasants better so they could move among them like "fish in water." Between this and the help he got from the Soviets (nearer and more motivated than the Americans helping Chiang), Mao was in a very strong position.
It was not inevitable. From one perspective, there was significant debate among policy-makers in the United States about the degree to which the US should aid Chiang Kai-Shek. US aid was sporadic though considerable, but if the United States had invested more in the conflict, things could have gone differently. It seems unlikely that Mao's army and his movement could have been completely defeated, but certainly the civil war could have ended on different terms than it did. Either way, it stands as one of the great human tragedies in terms of lives lost.