/i/ sound before "ng" and "nk"
Something funny happens to short i in some California accents; what most of us pronounce as short i (as in sit or king) turns into long e (as in seat or keen) when it's before an "nk" or an "ng". So ink would be pronounced eenk in these accents.
But this is a regional thing, established in California, Michigan, and probably several other regions of the U.S., but there are lots of regions where people don't do this. So the dictionaries are correct; except in California, pink and ring have a short i like bid.
Modern neutral American English often uses the long ee sound before nk and ng. It's not regional so much as it is just the evolution of neutral American English. For example, kin and king are completely different "I" sounds. But unfortunately many English learning materials still teach it as a short sound.
Also here in Maryland we say K-ee-ng (king) and p-ee-nk (pink). A google search actually brought me to this thread, because I had a similar question regarding my son's Kimdergarten homework.
Yes, for my money the "i" in "ink" and "ring" is pronounced long e. Like in "creak" and "leak." I don't get the short i pronunciation with these words.