In one of the OU's writers' conferences, someone had posted saying that she was unconvinced by free verse. Surely, she said, it was just prose broken up? She then posted an example which I haven't copied here, but it was a short paragraph of prose, broken up with short lines, as in a poem.
You've fallen into the trap of thinking that something is either poetry or it isn't. A black/white or on/off or head/tails kind of thing. But it's more like a spectrum with pure poetry at one end and pure prose at the other.
If you think of the dullest instruction manual or text book, that's pure prose and if you think of writing which has the richest metaphor, multilayered meanings, beautiful metre (and where appropriate) rhyme, then that's pure poetry. Most writing fits somewhere in between and novels can have passages that could be read as poetry and some poetry still works as poetry, even though it could be read as prose if you took the line breaks out.
What you first wrote was pure prose. Breaking it up shifted it some way in the direction of poetry. Re-written, with added metaphor, you might have something like I've posted below -- surely now poetry, even if not good poetry :-) A more skilled and experience poet could take my version and make it even more poetic. And so on...
This free verse thing
Someone has taken a pen,
Or perhaps these days
Put fingers to keyboard.
They've fished for ideas
In the shadowed pools of memory,
Tried to snag the fleeting thought
In a fragile net of words.
When they have finally hooked
What they want to say,
Avoided the snags
Of rusting bicycle wheels
And patiently untangled the thread
From the old abandoned
They must land the theme
Gasping and thrashing on the bank,
Similes and metaphors streaming
From its sides like water.
Then they must set out the words,
With capitals in the right place
Only to have people say,
"Not convinced at all,
By your fractured prose."