Doing business is orthogonal to being a company, and depending on your country, some "company" forms are just VAT filing registrations for an individual itself with no independent legal status. What you normally call a company is something that behaves as an independent legal person.
However, it may be legally required to register a proper company if your yearly business volume exceed a certain value - check local rules - but it may also be perfectly fine to do business as an individual below that volume, in which case the legal entity is just you.
(The alternative to being a business in a transaction is being a consumer)
No, you didn't read that wrong. It does seem like intention is that individuals cannot publish (publish, not write) software for playstore if they cannot operate as a business; Individuals actually can operate as a business as a sole proprietorship aka soleprop which can and do have a DUNS number and is a legit way of doing business. Individuals without any sort of business entity attached to them do not get a DUNS number attached to them.
Doing business and registering a company (a separate legal person) are orthogonal concepts that are specific to local legislation. You can do business as a private individual, and various "company" forms in various countries are not actually companies but just VAT/financial registrations for the individual itself and have no legal status of its own. Whether you need to register a company form depends on local rules and may be subject to e.g. volume limits (e.g., okay below 10k USD annual).
The alternative to being s business in s transaction is being a consumer (as in B2C), and you're obviously not a consumer when publishing an app.
