Tag (the game) = "Touch and Go"?

Solution 1:

It seems to me that "touch and go" is nothing more than a backronym (Wikipedia).

From the Online Etymology Dictionary entry for tag (n.2):

"children's game," 1738 (in reference to "Queen Mary's reign"), perhaps a variation of Scottish tig "touch, tap" (1721), probably an alteration of Middle English tek "touch, tap" (see tick (n.2)). Baseball sense is from 1912.

What raised my eyebrow more than that was I was today years old . . .

Solution 2:

According to this, the Touch and Go acronym is specific to competitive go-karting. https://acronyms.thefreedictionary.com/TAG