We could say that, in fact I'll say it now. If you remove the majority of your affiliate links, your site would be more likely to get a listing.
You'll notice that I've said "more likely", not "guaranteed". And that's the problem here, the review process is subjective. If you remove all but one of your affiliate links, but that one uses very large text, right in the middle of the page, the site gives the impression of being there to sell. I've seen some sites where they could have removed all of their affiliate links, and I still wouldn't have listed them. That's because all of the text on the site was designed to drive poeple to the affiliate links. Removing the links would have left just sales pitch, with no useful informational content. I haven't looked at your site, so I can't tell you if removing your affiliate links will get you listed. The editors that reviewed your site probably came across the affiliate links, and rejected there and then. They didn't look at the rest of the site, so they can't tell you if it's listable or not.
Generally speaking, sites are designed either to provide information, or to create traffic for affiliate sales. If your site wasn't originally designed to provide information, you're unlikely to get it listed just by cutting down the number of affiliate links. Remember also that we're all human here, and humans get suspicious. If we see someone cutting down the amount of affiliate links just to get listed, we get suspicious that they might put them all back once they are listed, and that means we check them regularly to see if our suspicions had any foundation. Sites discovered to be adding affilaite links after getting listed are terminated with extreme prejudice.