The cfinput validation you're attempting to do is the client-side equivalent to
<cfif len(trim(string)) gt 0>
(Edit: That is not to imply that you should depend wholly on client side validation. Client-side validation is more of a feature to help your visitors. Server side validation is still important.)
Which I have to say is really weak validation. Anything consisting of at least 1 non-whitespace character will pass the test. People will be able to have usernames like "!" which isn't fanstastic, but that's just some information.
On the jQuery Validate link you provided, they show an example form (along with a link of the same form in action)
<form class="cmxform" id="commentForm" method="get" action="">
<fieldset>
<legend>Please provide your name, email address (won't be published) and a comment</legend>
<p>
<label for="cname">Name (required, at least 2 characters)</label>
<input id="cname" name="name" minlength="2" type="text" required>
</p>
<p>
<label for="cemail">E-Mail (required)</label>
<input id="cemail" type="email" name="email" required>
</p>
<p>
<label for="curl">URL (optional)</label>
<input id="curl" type="url" name="url">
</p>
<p>
<label for="ccomment">Your comment (required)</label>
<textarea id="ccomment" name="comment" required></textarea>
</p>
<p>
<input class="submit" type="submit" value="Submit">
</p>
</fieldset>
</form>
<script>
$("#commentForm").validate();
</script>
This very basic example shows how simple Validate can be to install, and a simple format of
<input name="ele" type="text" required>
is exactly the same level of validation you're attempting. So, to begin with, you can almost copy and paste the code. (Aside from from the different requirements you can make, setting minlength requires a certain number of characters and requires that at least one not be whitespace).
jQuery Validate can get quite extensive but is very easy to basically install and once you become familiar, make custom classes as needed
As a final note, don't disregard the disdain for CFForm elements. It may seem like others are disregarding your question, but that's not the case.
To be honest, they began to be introduced at a different time in the life of the internet, but have always been kind of finicky to work with. Expansion to them, in the opinions of many, have not been done well and have frequently exasperated the flaws.
It's super attractive to be able to say <cfinput...required>
but the tags become a nuisance and you don't easily have the fine control over them that you might desire. They're a crutch, and a rusty crutch at that.
You might check out CFUI The Right Way @ Github or this hosted version for some great insight and examples.