What is this type of puzzle called? It’s where the way the words are arranged visually is itself a clue to the answer. Example:
Infini | tive
= “Split Infinitive”
I’m pretty sure I’ve seen them called “Wacky Wordles”. But I’m not finding much from Googling.
I would say it’s a type of rebus (which typically use pictures, but many also feature words or wordplay)
It’s a type of rebus often called a “frame game”.
Like:
HEAD
HEELS
(Head over heels.)
A typical rebus may be only words or letters arranged a particular way as a clue, or might include pictures as well.
If you Google “frame game” it gives many examples of rebus puzzles only showing words and letters.
Ah, and wiki sez : “A rebus made up solely of letters (such as “CU” for “See you”) is known as a gramogram, grammagram, or letteral word.”
You can say this for the human race : NOTHING will remain un-typified or unclassified. It is useless to resist. You will be nomenclatured.
And for a word nerd like me, that’s a good thing. A very good thing.
Except none of the examples on that page resemble what the OP was asking for.
Infini | tive
…is not a gramogram as defined there. A gramogram is much more narrow; you say letters and/or numbers aloud and pronounce a word or name. Kind of like how people try to squeeze a phrase onto a personalized license plate. The OP’s puzzle isn’t anything like that.
I’d agree it’s not a gramogram, I’d read the definition too hastily. But one of the examples of rebuses given on the wiki page goes something like
SECRET
SECRET
SECRET
(answer : top secret)
which is exactly like the OP’s riddle : words that can, if combined with nontextual contextual clues (here and in the OP : where the words are placed in relation to each other ; plus typography in one case and the addition of a | in the other), lead to a different word or expression.
Agreed, it’s definitely a type of rebus. 
Where is that maddening thread with the unresolvable letter clue?
I remember seeing one that claimed to be on an envelope that the post office was actually able to correctly deliver.
Down
John
Maine
Andover, Maine, is quite small, so I imagine it was easy enough for them to find John Underdown even without a street address.*
- I saw this given as an example of the type of puzzle being discussed. I have no idea if this actually happened.
Rebus is correct, they are also known as Dingbats (perhaps only in the UK, and I think it may be a trademark).
Started by a poster called mittu, the infamous 14 k of g in a f p d. But that was a ditloid, not a rebus.
BUMP
So what are puzzles called that spell out a phrase using symbols?
My son loves these and I want a book of these. Most Rebus puzzles appear to be just one picture, not a phrase.
That is definitely a type of rebus; the original “Concentration” had a pair of long puzzles like that when contestants were trying to win a car. They had to solve both within a certain time limit to get the car.
Your example resembles the puzzles in this book but I can’t tell if they’re single puzzles per frame or what.