I wouldn't say academic references are absolutely necessary. But certainly they are much more relevant than industry references. Usually, people from industry are not able to evaluate your potential to be an academic researcher since they don't have the knowledge and experience for that. I would consider them weak letters of recommendation. If it's just 1 from industry out of 3, for example, then I think it's still ok. But no letter from academia doesn't sound good.
You need to think how you could convince schools that you have great potential as a researcher. Because your profile is really industry-oriented. You may have a hard time even convincing them that you know what you're getting into.