Learn English – non-medical name for the curve where index finger and thumb meet

Though I am not familiar with any game name, there are phrases for what you are talking about.

Quid pro quo, meaning something for something, is a Latin loanphrase that indicates an equal exchange of information, goods, or services.

Other phrases with identical meaning are tit for tat, like for like, equal exchange, equivalent exchange of information, and several others which may easily be found by searching a thesaurus for 'quid pro quo'.

Line 4 is called the span or handspan.

span noun
1 the full extent of something from end to end; the amount of space that something covers:
...
(also handspan) the maximum distance between the tips of the thumb and little finger, taken as the basis of a measurement equal to 9 inches.

[ODO]

Merriam-Webster's definition of palm is based on your line 2: the breadth of the hand. Most people's palms are more-or-less square, and that distance is approximately the same as the distance from the wrist just below the ball of the thumb to the top of the palm at the base of the middle finger.