That jumping next to Kong's foot is allowed since there's a timer. If there was no timer, it wouldn't be allowed. You can pretty much jump next to any enemy and grab 100 ponits like that. Barrels coming down ladders, fireballs, in front of a pie, next to the spring as it passes by, etc. The one next to Kong's foot is probably a bug though, but if you get close enough to his foot, you don't even have to push the joystick. It's easy enough to do it by pushing the joystick though, and is much safer that way

From what I understand, when you push the joystick after jumping, it makes the enemy detection area around Mario much larger, so he would get points jumping over things. Using it to jump next to objects was probably an unintended outcome.
As far as ROM sets, for the US version, TG tracks set 1, not set 2. Set 2 is the one that only says "Nintendo" instead of "Nintendo of America" on the title screen, and also has the ladder bug, where you can sit at the top of a ladder, and the barrels won't come down on you. (if you ever come across a machine "in the wild" that just says "Nintendo", you'll know it's set 2

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(edit: changed set 1 and 2 around...TG actually tracks set 1. set 2 is the older set, called dkongo)