Learn Dutch: Het boek is goed, tenminste voor deze lezers. - The book is good, at least for these readers.

Here, tenminste restricts or nuances the first part of the sentence. The speaker claims the book is good, but then uses tenminste (meaning "at least") to limit that claim specifically to "these readers." It acts as a slight correction or condition.

Could I use minstens instead of tenminste here?

No, that would sound very strange. Both translate to "at least" in English, but they have different uses in Dutch. You use tenminste to correct, restrict, or nuance a statement, just like in this sentence. You use minstens for a minimum amount or number, for example: minstens drie lezers (at least three readers).

Why doesn't tenminste trigger an inversion (verb before subject) here?

Because the second part of the sentence isn't a full clause! It is just a prepositional phrase (voor deze lezers) added as an afterthought. There is no verb to invert here.

Could I use althans instead of tenminste in this sentence?

Yes, althans would work perfectly here and means almost the exact same thing in this context. Both althans and tenminste are used to restrict or correct a previous statement. Althans can sometimes sound slightly more formal.