I suspect that by AWS going first here, they can easily go for more integrations whilst also eating some of the Zapier's competitors lunch.
This depends on price and by that time its possible that Google Cloud Platform and Microsoft Azure will start jumping in on the integrations market too, further squeezing the likes of some enterprise-only integrations such as Tray.io which still has less integrations than Zapier in general.
It's still too early to tell, but we'll see how fast Amazon adds support for more API integrations or if GCP and Azure will join in and do the same.
Amazon seem to have a disadvantage here though. This kind of tool is aimed at non-developers who want to glue stuff together. With Zapier, they register an account and get stuck in – straightforward. With AWS, they register an account and are instantly overwhelmed with a million different things. AWS is too big and unfocused for the target market. I've seen developers hit a wall once they get on board AWS because it's just too much to deal with. You think the AWS dashboard is any friendlier to non-developers?