Should startup-company founder accept peer-review requests?
I think you should not take up this review, based on three reasons:

(1) No longer 'peer' : As an entrepreneur, you engage with technology, products and marketability more than academic research, thus defeating the purpose of peer-review, where researchers review papers in their field of work, and ideally get reviewed equally when they publish. The exception to this is if the journal is a technology journal focusing on product development and you have been asked to review from that perspective.

(2) Resource availability : To review a paper well, you will need access to related work in the field for judging correctness/suitability, possibly you will need to follow up some references, and more importantly, you will need to have time and current knowledge of published literature in the field. Unless the start-up is research-oriented, I think these resources may not be very accessible.

(3) Potential conflict of interest : This may not apply to the present case, but if this repeats, you may find yourself in situations where your review could be biased (eg. the paper reports flaws in a competitor's technology), and this would be an avoidable ethical burden.

Finally, the overbearing message I get from the question is that you are considering review because it could potentially benefit your product (through professional network etc). IMO, this is neither good (review should have a share-and-grow ethos) nor particularly effective- your network can be built better through more conventional routes, and also publishing a paper may not reach a big chunk of your target consumers (unless you are targeting the research community, in which case many of these points are invalid.).