The victorious force does own captured movable state-owned equipment and are acting within the law when they take it and are not looting - rule 49 of customary international humanitarian law, which has ancient precedence and is reinforced implicitly in both the Hague Regulations, Geneva Conventions, and pretty much any state's own military laws.
The local population have no such right - that's what makes it looting when they do it.
Since when are products in stores or the stores itself property of the state? Or personal property inside and outside houses?
I don't think they are. Why do you think they would be? The laws of war specifically exclude personal property.
That paragraph in the article is referring to for example 'musket, sabre, bayonet or ammunition pouch' on the battlefield. They're state-owned and aren't personal property. (Well, historically an officer's equipment might be personal purchase but I don't think the law would interpret any fighting equipment as being legitimately a personal effect.)
But the examples specifically given in the article from the battlefield aren't looting, and that's why the article doesn't say they're looting. But I won't keep arguing.