"Under section 162 of the Code, an activity does not qualify as a trade or business unless its primary purpose is to make a profit and it is carried on with regularity and continuity" (IRS - Which Employers are Eligible?).
Myth: Nonprofits Can't Earn a Profit
"Reality: The term "nonprofit" is a bit of a misnomer. Nonprofits can make a profit (and should try to have some level of positive revenue to build a reserve fund to ensure sustainability.) The key difference between nonprofits and for-profits is that a nonprofit organization cannot distribute its profits to any private individual (although nonprofits may pay reasonable compensation to those providing services). This prohibition against “private benefit” is because tax-exempt charitable nonprofits are formed to benefit the public, not private interests" (Myths About Nonprofits).
Owners & Employees
501c3 Nonprofit Organizations do not have "owners." So any W2 employee should qualify for the employee retention credit.
"A nonprofit corporation has no owners (shareholders) whatsoever. Nonprofit corporations do not declare shares of stock when established. In fact, some states refer to nonprofit corporations as non-stock corporations" ("Who Really Owns a Non-Profit?").
"501(c)(3) organizations are nonprofit groups with a dedicated mission. Most people are familiar with them as churches and charities, but they also include private foundations. As long as they operate to support their mission, they receive favorable tax treatment, such as avoiding federal income and unemployment taxes" ( Investopedia).
Employee Wages
"Exempt organizations normally withhold and pay employment taxes under the same rules as other entities. Like other employers, section 501(c)(3) organizations that pay wages to employees must withhold and deposit federal income tax and Social Security and Medicare taxes from employees’ wages, and pay the employer’s share of such taxes" (IRS Article - see Additional Reading).
Types of 501c3 Nonprofit Organizations
"Organizations organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, educational, or other specified purposes and that meet certain other requirements are tax exempt under Internal Revenue Code Section 501(c)(3)" (IRS - Exempt Org Types).
Additional Reading