Verb reduplication of
指 (zhǐ, to point). Reduplicating a single-syllable verb softens it into a brief, casual action — 'to give a quick X' or 'to X a bit'. Compare
看看 (kànkan, take a look),
想想 (xiǎngxiang, think a bit). Almost always paired with
指点点 in the chunk
指指点点 (zhǐzhi diǎndiǎn, 'to point fingers and gossip').
