I think this may be a documentation error, since the docs state that URL is required, but do not provide an option for an ID on its own. The example on the page shows the URL parameter being used with the full link to a Tweet:
GET https://publish.twitter.com/oembed?url=https%3A%2F%2Ftwitter.com%2FInterior%2Fstatus%2F507185938620219395
There is a workaround, if you only have the Tweet ID. Here’s an example:
twurl -H publish.twitter.com "/oembed?url=https://twitter.com/twitter/status/1008419070524448768"
In this case, Tweet ID 1008419070524448768 actually belongs to my account. The returned oEmbed resolves to point to my profile - it does not matter which user handle is included in the URL.
{
"url": "https://twitter.com/andypiper/status/1008419070524448768",
"author_name": "Andy Piper (pipes)",
"author_url": "https://twitter.com/andypiper",
"html": "<blockquote class=\"twitter-tweet\"><p lang=\"en\" dir=\"ltr\">Mmm. <a href=\"https://twitter.com/bigfinish?ref_src=twsrc%5Etfw\">@bigfinish</a> sales are gateway drugs to so much good stuff I haven’t yet heard (or read!).</p>— Andy Piper (pipes) (@andypiper) <a href=\"https://twitter.com/andypiper/status/1008419070524448768?ref_src=twsrc%5Etfw\">June 17, 2018</a></blockquote>\n<script async src=\"https://platform.twitter.com/widgets.js\" charset=\"utf-8\"></script>\n",
"width": 550,
"height": null,
"type": "rich",
"cache_age": "3153600000",
"provider_name": "Twitter",
"provider_url": "https://twitter.com",
"version": "1.0"
}