Depreciation recapture is only required if you take the home office deduction and use the actual expense method instead of the safe harbor method. It has nothing to do with a business license or even if you have self-employment, only if you take the deduction.
Separately, your spouse is required to report self-employment income regardless of whether or not he has a license; he is self-employed if he is engaged in an "ongoing trade or business" regardless of any state licensure requirements. And if he is not engaged in an ongoing trade or business, the income still has to be reported as hobby income. The main difference being, you can't deduct business expenses from hobby income any more, because that is a miscellaneous itemized deduction subject to the 2% rule; and self-employment is subject to the additional 15% self-employment tax.
There is no simple definition of being in a business or hobby. Some of the factors to be considered are diligence in pursuing business opportunities, whether he advertises himself and seeks new business, the regularity and consistency of the income and work opportunities. It can be considered self-employment if it is only part-time, as long as it is something he "regularly" does. If he has a hobby and regularly reports income each year, the IRS may eventually wonder if that shouldn't be reported as a business and pay the extra self-employment tax. If he reports it as business and his expenses are more than his income, you can deduct the loss against other income, but if he has too many losses, the IRS may decide that it is a hobby and stop him from deducting his losses. (They don't want you reporting a hobby as work, and they don't want you reporting work as a hobby.)
