Can you explain this? If someone has a bundle of cash from illegally selling drugs, then they give it to their store front to "launder" as retail income, aren't they now paying tax they wouldn't otherwise pay?

When you earn your income, you pay a tax, and when you spend it, the business pays a tax.

In money laundering, only the retail business pays the tax, so effectively its not the equivalent taxation.

Why would there be personal income tax on the criminal activity? Guy sells drugs but obviously can't record the profits as DrugCo's profits, so he records it as RetailCo's income. If DrugCo was legal, the taxes would be on that company instead. His personal income tax is unchanged: whatever he takes out of RetailCo is still taxed, and RetailCo pays whatever corp taxes are applicable.

The only difference is in the details of the corporate taxation. Selling meth legally might be taxed differently than laundromat services. So an ethical money launderer should look to use front businesses that have an equivalent tax rate and not take advantage of any special tax discounts that wouldn't apply to the original source.