Lots of sophomoric comment here, but where are the facts?
Does the chemical structure of rubber change with age? Not really. Much like the chemistry of cheese does not change by either removing or adding water. The chemistry of rubber changes with the addition of UV energy, or exposure to certain chemicals.
Is the tyre still "curing" or has it cured and the evaporation is a simple mechanical one? The tyre's chemistry is 99.99% stable after it has cured. Wrap a tyre in plastic and keep it away from UV energy and the tyre will stay supple a very very long time. So, what is evaporating as a tyre ages? Its a very rather complex mixture of acids, ketones, and VOCs. Much like beans can be reconstituted with the addition of water, tyres should be reconstituted with the addition of this evaporate.
Are the chemicals in the advertised product changing the chemistry of the tyre? Bleach, for example alters the chemistry of rubber; it breaks down the nitrogenous and other protein-like compounds in natural rubber, unraveling the polymer chains and reducing its ability to stretch without fragmenting. Gasoline works by dissolving the polymers in solution and hence weakens the bonds that way. How does this chemical work? Is it a solvent, a rebinding agent, a polymerization enzyme...?
Answer these questions, and the mystery will be solved without more sophistry.
Edit: Keep in mind that if a tyre has aged and then through mechanical manipulation the rubber has cracked or pitted, then reconstituting the rubber will still not re-bond the cracks or fill in the pits.