The idea that walking made us human probably seems naive these days. However, tools, fire and language followed much much later - and the significance of walking gets quite a shot in the arm from memetics.
As I explain in considerable detail in my 2011 memetics book, walking was one of the earliest socially transmitted traits in our ancestors. The need to walk put pressure on infants to master the social skills needed to learn to walk from their parents and caregivers.
Chimpanzees socially transmit use of tools such as hammers. However, there's nothing similar to walking in demanding early learning and so profoundly affecting development.
It was walking that kicked the race to develop social learning into a high gear in infants among our early ancestors. There was cultural transmission before walking - but is wasn't so profoundly life-changing. It is true that the expansion of the human cranium corresponding to colonization by memes didn't begin for another three million years - but that seems consistent with walking having a high significance in the development of social learning. Walking generated pressure for social learning skills to develop early. It was a while before this started having knock on effects that led to an expansion of the meme pool as the size limit on cumulative cultural evolution in our ancestors gradually began to rise.