There are so many problems with this video.
Is he asserting that private property and/or enforcements of contract are exclusive to capitalism? Untrue in both cases. Are these 2 features of capitalism? Yes. Are they the only features? No.
There are many different defintions of capitalism (or types of capitalism, depending on how you choose to see it). So, he is partially correct in identifying that the people who reject it may be opposed to only a certain type of capitalism, or that they are only opposed to certain aspects of it.
The most widely practiced form of capitalism (and therefore likely the type the respondents were basing their response upon) is free market capitalism. There are many things that a person may reject in this type of capitalism - its history of market collapse, widening of inequalities, exploitation of wage workers and the list goes on.
Given the popularity of movements like the Occupy cause, which oppose this dominant type of free capitalism - it is quite reasonable to presume this is the same sentiment being reported by the poll takers (at least it is not any less reasonable than the video's presumption that they rejected only preivate property and contracts).
In any case, only a study that clarified what "capitalism" meant to the poll-takers could ever be seen as a valid and accurate picture of what those poll-takers opinions were. In the absence of this, the study would be pointless. I have not read it, but I do recall it was performed by Harvard. One would pray they are competent enough at research design to have considered this.
To say capitalism is "only" about a right to private property and compulsion to uphold contract is one of two things: uninformed, or dishonest (ie politically motivated).