I thought it might be helpful to re-post this original question, because I have been fascinated by some of the comments, and truly appreciative of those who have responded to defining terms of which I was unfamiliar, thanks for those.
The fascination part(s) come from what I consider extraneous mention of items such as:
--- mark rounding - the OP makes no mention of being close to a mark and has no bearing on his question
--- starts - no bearing here
--- parallel courses- impossible given the question
--- puffs, lulls, other boats - not mentioned, nor relevant to the question
--- HunterbeneteaucatalinaJboat is immaterial. Why? W is sailing a beam reach. L is sailing higher - almost any boat could! They were both in the same race.
Basically, John's post which highlight the, uhm, highlights of the question.
To me, I tried to simplify this to: let's say W is sailing due west 270, his tack (port or starboard) doesn't matter, wind is from either north (or south) 'cuz he said he's beam reaching, to what I believe we can consider a distant mark
BUT he is on his layline. For our purposes, let's say the wind is from the north.
The L boat is coming up on his port side steering 290, and he is sailing higher because the proper
course to the distant mark for W is a reaching course. This is regardless of how the course is or was set to the wind;
it is where he and the other competitor are AT THAT POINT IN TIME. (Ever sail on an empty lake and find a hour later that the ONLY other sailboat on the lake is going to end up in exactly the same place as you're gonna be?!?

).
So, back to the question:
1. Should L have given way? L could have made the mark by falling off earlier and avoided W altogether because from where L was earlier he could have laid the mark because of the wind direction (not because he was in a boat that could point higher than W).
2. Should W have given way? A simple windward/leeward question for boats on the same tack (they had to be on the same tack or else the question wouldn't make sense).
I don't know the answer, but have simply tried to, uhm, simplify the question and weed out the stuff that has no bearing on the question.