As far as I know, the last link in a Tweet is embedded in the Tweet. This is how embeds appear from a Twitch Clip and Twitter knows how to get the embed because of <meta> tags in the HTML of the link:
<meta name="twitter:card" content="player">
<meta name="twitter:site" content="@twitch">
<meta name="twitter:image" content="https://clips-media-assets.twitch.tv/151570779-preview.jpg">
<meta name="twitter:player" content="https://clips.twitch.tv/embed?clip=DifferentDeafKuduCopyThis">
<meta name="twitter:player:width" content="640">
<meta name="twitter:player:height" content="360">
<meta name="twitter:image:partner_badge:src" content="https://clips-media-assets.twitch.tv/img/twitch-white-rgb.png"/>
There’s also “watch_now” in the “call_to_actions” section in the Twitter API (statuses/show/:id) at tweetData.extended_entities.media[0].additional_media_info.call_to_actions.watch_now.url which I presume is how the embed’s overlay gets the “Watch now at twitch.tv” text’s href.
All you have to do on Twitter is to post a link to a Clip and it’ll be magically embedded in the Tweet.