If you don't use namecheap's dns servers, dns requests for your domain do not go to namecheap for redirection. They don't go to namecheap at all. Your specified dns servers get registered with the top level domain servers.

If you use Route 53, your zone file is still at Namecheap (registrar). Doesn't that still make Namecheap a failure point?

No. The zone file lives on the nameserver (DNS server) which Route 53 provides. Namescheap registers a list of nameservers for your domain with the TLD.

An over simplified example for looking up "news.ycombinator.com":

1. First query the TLD nameserver for all ".com" domains asking for the authoritative nameserver(s) for "ycombinator.com".

2. Next query that nameserver for "news.ycombinator.com".

But, the first entry point is namecheap. The domain is at Namecheap, so it will not find the zone file at Route 53, if Namecheap does not send it there. Right?

No, registrar's are your portal to updating data in TLDs, but those TLDs are each operated separately. .com and .net are operated by Verisign, for example.