As a Marxist analysis this makes sense, and puts Toy Story firmly within the tradition of mainstream Hollywood cinema and particularly in children's features.
Where I think it is not complete is that it rather ignores the reason why so many people have been critically admiring of it. As a criticism it looks at the fundamental structure of the narrative and characters rather than the plot.
The thing about Toy Story 3, and what makes it a blub-worthy* film, is that it is a coming-of-age tale, or perhaps more specifically a rite-of-passage movie. The story is of the toys coming to terms with the loss of their owner, because the owner has outgrown them. Of course, as adults we recognise our own experiences of finding oneself too old to play, of having to put away childish things. In Toy Story 3, Andy does so without regret but with a sense of loss - which I know I could identify with. And as with Andy there was one toy which I didn't want to leave behind me, and which has survived all the moves back and forth around the country more or less intact, though usually just stuffed in a box somewhere and never actually out on display.
For Lenin, our attachment to toys is a symbol of our sick late-capitalist culture, where we attach affection and recognisable cultural tropes to inanimate, mass-produced objects - things incapable of returning our love and identical to the playthings of millions of others around the world. There is some truth in this of course, but not a whole truth.
Humans, I think we can all agree, are natural anthropomorphisers. You can see this in the polytheistic societies of ancient Greece, the medieval anthropomorphic personification of Death, and in what Daniel Dennett calls 'the intentional stance' (the idea that we adopt towards people an expectation that they will behave as though they have beliefs and desires and that this is a stance that can be adopted towards non-human things as well, on occasion). So in the way in which people play with toys Pixar have it right - especially as children we simply do bestow inanimate objects with intentionality and personality. The fact of the means of production of these objects is not relevant as an object of conscious experience to the child playing with them.
Some Marxists deny that there is any such thing as 'human nature' and of course human nature is a lot more flexible than is sometimes assumed.** Nevertheless there are some behaviours that humans engage in pretty much universally, and one of these is play. The actual form of play is culturally determined, but the act of play is not (although the extent to which play is encouraged or denied is - the point here is that given the opportunity, children play, by themselves and in groups). In American and other late capitalist cultures the form of play is recognisable in Toy Story and therefore provides the familiar cultural context to the theme of maturity and loss to engross an audience in the story.
Some reviewers have pointed out the comparisons with Winnie-the-Pooh in this theme. Winnie-the-Pooh offers a similar, though notably less commodified theme when Christopher Robin tells Pooh that he will have to go off to school, and won't see so much of him any more.
Vygotsky, in his essay on play, says that
play is such that the explanation for it must always be that it is the imaginary, illusory realization of unrealizable desires. Imagination is a new formation that is not present in the consciousness of the very young child, is totally absent in animals, and represents a specifically human form of conscious activity. Like all functions of consciousness, it originally arises from action. The old adage that children’s play is imagination in action can be reversed: we can say that imagination in adolescents and schoolchildren is play without action.Play therefore is fundamentally developmental, and the leaving behind of a particular way of thinking, which is to say a way of life. This acknowledgement of change and loss is the heart of Toy Story 3, regardless of the bastardised culture that it finds expression in.
Judging from the scale of its box office it seems to do this rather well - although the extent to which people identify reasons for seeing it with this portrait of change is of course arguable - but I do think that any analysis of the film that leaves out this dimension to the story has missed something fundamental.
* I should probably add my personal attitude to Toy Story briefly. I have a great deal of fondness for a lot of the Pixar films (Up and Wall-E especially) but I have no great memory of the first 2 Toy Story films. I went to see Toy Story 3 and enjoyed it a lot, but not, if I'm honest as much as Up or Wall-E. Still had a (manly) tear in my eye at the end though.
**I don't just mean 'God created Adam and Eve, not Adam and Steve' type moronicism, but rather that without a considered critique of the role social institutions have played in our development we have not really begun to approach what that nature might consist of and are instead lazily applying culturally loaded ideas like 'humans are naturally greedy'. For a good discussion see here.
N.B. I've edited the bit on anthropomorphisation slightly as I realised that the whole paragraph had become somewhat sidetracked into human nature a bit prematurely.