I'm not sure exactly what is in "Staticide," since their formula is proprietary. However, some people do use solutions of fabric softener to reduce static electricity. It is the same chemical that is in fabric softener sheets that you can put in the dryer with your clothes. The chemical that allows fabric softeners to reduce static electricity is typically a molecule like dipalmitoylethyl hydroxyethylmonium methosulfate. It is a molecule with two alkyl chains and a quaternary amine - but what does that mean? The alkyl chains (the part where it says di (two) palmitoyl (12 carbon chain)) are hydrophobic - they like to bind to proteins or lipids, which is how most soaps work (why it likes to bind to carpets, etc). The quaternary amine is a cation - it has a positive charge. This type of molecule is called a surfactant. It will bind to something hydrophobic, but the positive charge can neutralize any charges built up, which causes the static electricity.
There are also other types of molecules - anionic lipids. These would have the same long-carbon chain (alkyl group), but attached to a phosphate group, which carries a negative charge.
To reduce the static electricity, you bring in charged molecules, which neutralize the built up charge. By making the charged molecules also hydrophobic, it makes them easy to disperse, like a soap.
I hope that helps!