Academic papers are generally written to be read by peers in the field. If you're not a researcher in the hypermedia field, you shouldn't expect to immediately understand a paper without doing some work. The abstract is a paper distilled to its essence, and is not the place to expect to learn the necessary background.
In this case, the abstract says: "This functional mechanic is used to create first an informal and then formal definition of the term "hypermedia control". Using this formal definition we then derive a generalization of the concept, referring contextually to the World Wide Web." Therefore, we should expect to look in the paper for the definition.
We find the "functional definition" at Definition 4.1: "A hypermedia control is an element that responds to an event trigger by issuing a type of request to a URL and placing the response at some position within the user agents viewport." The "formal defintion" then follows immediately after, but can't be quoted here because it requires LaTeX notation and a full page of text.
As a possible non-academic summary is that a hypermedia control can be defined as:
An interactive element within a hypermedia system (like a web page) that allows users to trigger actions, typically resulting in new content being loaded or displayed. Common examples include: links (clicking loads a new page); buttons (clicking triggers an action like submitting a form); form inputs (entering data and submitting retrieves results); images with embedded links (clicking loads new content).
The key aspects of a hypermedia control are that it responds to a user action (click, submit, etc.); it causes some kind of network request (usually to fetch new content); it specifies where that new content should go (replace the whole page, update a specific area, etc.)
One important clarification I should have mentioned: buttons and form inputs only meet the definition of hypermedia controls when HTMX or something similar is used. Under normal HTML only links, images, complete forms, and iframes qualify, since (for instance) form inputs and buttons can't on their own make a request or specify where new content would go.
You can put the actual definition on page 4, or you can make it easy for the reader and just say "hypermedia controls (like links and buttons)" the first time you mention the term in the abstract.
Strictly speaking, buttons aren't typically hypermedia controls. Haven't read the paper yet but the only controls in HTML are links and forms. Buttons can be nested inside those as actuators but aren't controls unto themselves since they don't meet that functional requirement of sending a request to a URL and inserting response content into the viewport.
EDIT: It seems the authors also consider images and iframes to be controls since they also make requests and add content to the viewport.
In this case, the abstract says: "This functional mechanic is used to create first an informal and then formal definition of the term "hypermedia control". Using this formal definition we then derive a generalization of the concept, referring contextually to the World Wide Web." Therefore, we should expect to look in the paper for the definition.
We find the "functional definition" at Definition 4.1: "A hypermedia control is an element that responds to an event trigger by issuing a type of request to a URL and placing the response at some position within the user agents viewport." The "formal defintion" then follows immediately after, but can't be quoted here because it requires LaTeX notation and a full page of text.
As a possible non-academic summary is that a hypermedia control can be defined as:
An interactive element within a hypermedia system (like a web page) that allows users to trigger actions, typically resulting in new content being loaded or displayed. Common examples include: links (clicking loads a new page); buttons (clicking triggers an action like submitting a form); form inputs (entering data and submitting retrieves results); images with embedded links (clicking loads new content).
The key aspects of a hypermedia control are that it responds to a user action (click, submit, etc.); it causes some kind of network request (usually to fetch new content); it specifies where that new content should go (replace the whole page, update a specific area, etc.)