I know this video is a little old, but why does this work?
https://www.youtube.com/watch?v=74CA9BlFn-kNormally an item timer is supposed to restore the sword (or whatever is in temp b) when it warps you away if b is a non-sword item. I guess that only happens when the clock actually ticks down from 1 to 0, but not if you unfreeze a frozen timer? If that's the case, then why wouldn't this work with other minigames?
I looked into it and it kind of makes sense. He got the rod with master sword on B so when he first entered the shop these were his values:
B: 60 (master sword)
Temp B: 255 (blank/empty, used in shops to dim b)
When he got the rod the b button no longer needs to be dimmed of course so the item on B gets pushed to temp B and rod (89) goes on B.
B: 89 (rod)
Temp B: 60 (master sword, restored when quitting the minigame)
When the screen begins to fade into white, temp b is restored to B. So temp B and B are both at 60 (master sword) during the white fade-out.
B: 60 (master sword)
Temp B: 60 (master sword)
However, if the text box is canceled fairly quickly after this fade-out starts, the item that was on b (in this case the rod) is restored to b yet again (despite not being on temp b at the moment, interestingly). So now you have this:
B: 89 (rod)
Temp B:60 (master sword)
Because the fade-out already started and thus the temp b item has already been pushed to B, it does not happen again and allows you to keep the rod during the warp.
It appears the the stopped timer allows you to keep B button items on B despite running out of time if you cancel the text box before you are warped away. The reason this works is that the text from the trade item cannot come up on screen because there is already text on the screen. Also, while testing this, I figured out you can do it without talking to the guy twice. If you get the white fade-out to begin before the rod is placed on B then manage to cancel the last text during the fade-out, it will warp you out with the rod still on B
So now that I've explained that I can address your other questions.
This does not work on the archery games because the temp B item is pushed to B before the text from the archery guy comes up. You already have you temp B item back on B before the warp starts.
The Chu minigame is more likely to work but there is a text box at the end telling you what you are playing for that causes the white fade-out but does not allow mashing to get past, making it impossible to get into the game and talk to her before the white fade-out begins.