Only a rich text field can have that kind of formatting.  And only long text fields can be in rich text format.  Thus, short text and numeric fields can't be highlighted that way.  Also, such formatting is part of the field's content in the table.  You wouldn't want to alter the table's content just to do highlights.  In short, it's a difficult, if not an impossible task.  You could show a bunch of dummy rich text fields as the search results, but that would be cumbersome.

Find in Text Box
Find in Text Box 2

These videos show how to highlight the search term, but one at a time.
It uses a Find First button to find the first occurrence, then a Find Next to find the others in turn.
This is similar to how the built in Find dialog works.

Yeah, it's certainly possible with a Rich Text Long Text field. You'd basically do a Replace inside the field's HTML, wrapping the matching search text in a span with a background color. Of course, as Kevin Yip pointed out, that means you're altering the stored value, so you'd want to be careful to use a dummy field.

That said, this has the makings of another video. Someone on YouTube asked me the exact same question recently, so I'll add it to the list.

Definitely possible to show it in a 2nd rich textbox:

Notes2 = Replace(Notes, Search, "<font style=""BACKGROUND-COLOR:#FFFF00"">" & Search & "</font>")

Where Notes is the yellow regular textbox, Search is my textbox that has "Spock" in it, and Notes2 is the rich textbox showing the results.

Can we expect a Tech Help on this?

Absolutely. I'm working on a continuous form now.

And lo, there was much rejoicing. Yay!

Yeah. That is very cool.

Now the pattern will get broken if your source text box is a rich text box and you already have formatting that spans over the search term. There's nothing I could do about that because I'm basically embedding HTML codes into the text itself. I'll explain exactly how in the extended cut.

The work involved is not trivial, so it's only worth doing if you have a lot of really long fields, which most databases don't.  I would say most fields in a typical database are short text like name and address fields, where everything in a short, single line so the matching text is plainly seen.

Also, a long text field with lots of text may have rows hidden, and the matching text may be hidden unless you scroll down.  Do the users need to scroll down themselves to see the matching text, or do you automate the scrolling with code?  And you can't scroll on a rich text field: Scroll Wheel Rich Text.  This seems more headaches than it's worth.