I wanted to add one more important detail not explicitly stated in the other answers. You said this:
It works by sending the server some crafted payload, which makes the
server code throw an error, and due to lack of error handling - It
crashes (until someone runs it again).
(emphasis mine). That caveat is important because the way such services respond to a crash can vary wildly between technology sets.
Not a DoS
For instance in PHP or most cgi implementations, a single crashed request has absolutely no impact on other requests. The server fails to send a proper response for the crashed request, but other requests coming in from legitimate users continue to be handled properly by the server. In this case the crash only affects yourself - not others - and so it would be hard to qualify that as a DoS attack. Sure, there is a bug, and you are denying yourself service, but if the server continues to operate normally for everyone else then there isn't really any denial of service going on.
If, however, your payload causes the actual service to go down and no more requests can be received by the server until some action is taken to restore services (whether by an admin or automatic restoration after a short period of time) then you definitely have a denial of service because the crash you caused stopped the service from responding to legitimate users (as discussed in other answers).
Under some circumstances the "Not a DoS" attack that doesn't take down the server could possibly be promoted to an actual DoS attack if you can "trick" a legitimate user to visit a URL with your malicious payload. Most of the time though such attacks don't have much practical impact since the service will continue to operate normally when they later use the service normally. However there could be rare circumstances when the payload is persisted to the session and therefore permanently locks out the user (I've seen people accidentally trigger such circumstances in real life before).
From your description, it's hard to tell which of these categories your particular payload falls into, but there is an important distinction to be made.