Was it Steve Yegge who menationed the Perl community calling Design Patterns "FP for Java"?
https://sites.google.com/site/steveyegge2/singleton-consider...
(define (make-counter n)
(lambda (c)
(set! n (+ n c))
n))
This is a HOF, but not an instance of Strategy.call/cc does not actually use the passed in function to determine how any action should be done. All it does is provide a capture of the current continuation as an argument. That's it. So it's not a strategy, it's just a HOF.
And semantically, a continuation is pretty much never a strategy.
As for make-counter not being higher-order, that's just not true. A higher-order function takes and/or returns a function. make-counter returns a function: it's higher-order.
Callcc can be implemented as a function, no continuation primitives needed. Haskell has examples in its libraries.
Lastly, regarding semantics, I see no difference between Strategy and a second-order HOF. Yes the scope of Strategy is supposed to much more limited, but I don't see value in this. I concede that others might do.
In that case, your lambda object is your strategy. One of the good points that the "Design Patterns" authors make and that everyone else ignores is that these patterns are names for recurring structures that pop up independently of implementation language and environment. Some silly functor object is one way of implementing the more abstract "Strategy" pattern. Your lambda is a better one in many cases. It's the same high-level concept.