Considering it does NOT look to support inbound or voice probably very little impact. (edit) i some how always forget the most important NOT operators.
Also, SMS is a substantial part of Twilio's business. Even though Twilio has been adding new extensions to their product, the majority of usage is tied to a small set of API calls.
Twilio now has a company with a huge developer audience going straight after their core business. One that is willing to be very aggressive on price to win share.
Sure, they have the developers today, but if WhatsApp leaves, and Amazon can cross-sell more of their existing customers what they'd otherwise get from Twilio, that's a big problem long-term. Twilio has a bit of a moat with their carrier/provider relationships, but that won't hold up against Amazon's entry.
Time will tell, I guess. The stock has been going crazy the past few days, though