Moving from business to academia I've been working in commercial software development for quite a while for now, and I'm getting more and more disappointed in the way things are being done here as time passes. 

So I was thinking to get back to academia, but the problem is that even though I hold master's degree, I have just a couple of publications (rather weak, I suppose), and there are no letters of recommendation in my disposal. Moreover, all colleagues I can possibly reference are engineers, not a scientists. 

Basically, I'm quite used to applying to jobs I do not fit entirely (I mean not 100% of requirements met) judging by their requirements list in commercial sphere, but how mandatory publications and references are? My estimation is that I'm still capable of at least supporting research project as a engineer, while regaining lucking researcher skills.
You question whether you satisfy the requirements for a position as a PhD student. The minimum requirement for such a position is a bachelor's degree, albeit, many positions will require a master's. You satisfy both of those requirements, so your move from software development to academia is entirely plausible. 

You seem to believe that publications are required for a PhD student position. They are not, at least, not at many institutes. They are nonetheless useful, even "just a couple," even if "[they're] rather weak," since they demonstrate an ability to do research and an understanding of the research process.

You are concerned that your referees are engineers, rather than scientists. This isn't a problem, actually it is an asset, as is your software engineering background. Impact is a measure of success in academia and your real-world experience can guide you towards practical research problems that have more potential for impact.