Yes, we're getting dangerously close, but we're not there yet. These corporations currently co-exist and collaborate with/ compete with national governments and must at least give the appearance of operating within the bounds of national legislatures and their own interim, international legislatures. Read up on TTP, TTIP, RCEP, FTAAP and AGOA to examine how such constraints are being removed. Then envisage the obvious next step. Once corporations can override the laws that we, the people, are constrained by they essentially have more rights than we do. History consistently tells us what happens then. The TL/DR answer is, we'll have regressed to feudalism but this time not based on the supremacy of God, but the supremacy of man (or worse).
The coming world will be like Star Trek. Yep, that's how protesting students convince themselves. In reality, there will be fewer of us (far fewer), we'll live in tightly confined spaces under even tighter control and all our decisions will be made for us and our requirements catered to us by a specialised and separate class that refers to nobody and answers to nobody. It will probably be a peaceful world (under pains of instant death for transgressors), with less suffering on a surface level (for those who comply), but it will also be a mentally disabled world of silent torment where everything that makes us human has been stripped away. History again intervenes to show us what this is like, if you think of the plantations in the deep south of America during the time of slavery, or the English peasant on his rented land working every hour to pay that rent.
What are most people fighting for today? Their dignity and freedom? Or an upgrade to their iPhone? They'll even campaign bitterly and turn against their own, such is their urgency to install the bars of the emerging prison.