For most startups the PM role is fulfilled by the founder's vision. However, as the company begins to grow and the initial vision is achieved, it becomes harder to go without someone focusing on the product aspect.
The reason someone like Stripe can do just fine without PMs is for two main reasons:
1)Incredible market pull - they just need to be methodical about following the requests and prioritizing them in accordance with revenue/implementation sequencing/risks.
2)Stripe's engineers are the target market - Stripe is built by developers for developers to make payments easy. Much like Jobs embodied his own target market, whenever you are building something for yourself, market research becomes a bit less important... more implicit.
If the above conditions are true for your startup, then absolutely, you can follow the example. However, if you are missing either, you should really consider dedicating someone to this research and visioning.