I'm not going to get into the grammatical nuances, but there's a simple grammar trick to figure out if something is saying what you think it does. Swap one word out with a word of similar type.
So instead of "Allowing two throws from close range to hole out", let's go with "allowing two throws from the teepad to hole out", or alternatively "allowing two throws from inside of the circle to hole out". Do you still believe that the two throws are defining close range?
Close range is completely undefined. The only logical way to assign any special meaning to it beyond common usage, would be to look at the intent of authors of the rule. As far as I know, nobody knows what this is. The best guess I heard is from Steve, with his suggestion that it is a homage to ball golf par. Well if that's the case, it clearly means the green, or at the minimum, the distance from which someone would attempt a putt of some sort.
I'm all ears if someone has some other insight into their intent. So far all I've heard is, "it must be 2 shots because 2 shots was mentioned elsewhere in the same sentence", which doesn't make any logical sense that I can see. And then somehow, this 2 shots is being stretched to the maximum distance where up and down can be confidently made, in spite of the fact that a pro player is probably expecting to make no better than a 2 all the way into 100 feet or closer.