They are seeing it as commercial use because those alternative apps have their own advertisements from which they make the majority of their money, which is specifically banned under the new terms.

Ads have nothing to do with the API changes. First of all, there's bot, to which ads are completely irrelevant, yet they're still affected by the API changes. Second, although there are 3rd party Reddit apps with ads, not all do. For example, Infinity for Reddit is ad-free (and open source), yet they're also affected by the API changes. In fact, Infinity's only monetization is via Infinity+, which has no extra features whatsoever, and only exists as a way to support Infinity's developer. Ads, or monetization at all, should have nothing to do with this.

Edit: sorry if I phrased something badly or was contradictory, I'm a bit tired :P - good night!