If you take something that belongs to another person, but you believe you do own it, no crime has been committed. For example, if walk out of a store thinking you paid for a bag of groceries when in fact the card reader had errored and you need to swipe again. That isn't shoplifting, that is a mistake of fact.
This concept is called "mens rea" or "guilty mind". A statute for each crime should define what type of mens rea it requires. As an example, generally murder requires an intent to kill or seriously injure someone. Manslaughter only requires a reckless disregard for whether or not you've harmed someone. However, some crimes do not have a mens rea requirement. They are usually minor, like speeding.
Actually that is not quite right. Some crimes require both "mens rea" (intent) and "actus rea" (action) but some require just "actus rea".
For instance, murder requires both intent and action but manslaughter only requires action. Which leads to the canonical law school example of a hit man who shoots his victim with the intent to kill him but the victim does not die. Mistakenly thinking the victim is dead, the hitman leaves the body in a deserted spot in the woods whereupon the victim finally dies of exposure. The hitman technically did not commit murder because when he shot the victim, he intended to kill him but did not actually succeed. However, when he did finally kill the victim (by leaving him out to die of exposure), he had no intention of killing the victim (because the hitman thought the victim was already dead).
Of course, this is all theoretical and if you did try to pull off a crime by manipulating mens and actus rea, you would find prosecutors very creative in finding ways to throw the book at you.
But in a case of property dispute, this contradicts what you said about the mind of the victim not mattering. If I am in your house and believe that the playstation is mine and walk out with it. Weather or not it is a crime is entirely dependent on what you believe about ownership of the playstation. Entirely on "whether or not the victim feels they were wronged".
No, the mind of the perpetrator is relevant, not the victim. And it isn't just "he said, she said", but the court tries to actually understand what was going on in the perpetrator's mind. For example, you can't shove merchandise down your pants at Walmart, sneak out the front door and claim "I thought it was mine".
It's a vital protection. Look at how messed up anti-money laundering enforcement became in the USA after the PATRIOT Act removed the mens rea requirement.
This concept is called "mens rea" or "guilty mind". A statute for each crime should define what type of mens rea it requires. As an example, generally murder requires an intent to kill or seriously injure someone. Manslaughter only requires a reckless disregard for whether or not you've harmed someone. However, some crimes do not have a mens rea requirement. They are usually minor, like speeding.
For a better explanation of mens rea, see this part of the linked site: http://lawcomic.net/guide/?p=173
EDIT: For an interesting example of when the mens rea requirements for a crime are unclear, see Elonis v. US: a free speech case involving intimidating speech posted to Facebook. http://www.scotusblog.com/case-files/cases/elonis-v-united-s...