Does anyone remember a computer game in the early 1990s that was based on the Alice in Wonderland adventure

I'm not sure if this is the exact answer you're looking for, but in the sixth installment of the King's Quest series, Heir Today, Gone Tomorrow (1992), there are quite a few references to the Alice adventures. In the game there's kingdom called Chessboard Land which is guarded by two rooks-- one white and one red-- and reigned over by two queens of like colours to the rooks. And, upon a table in lush garden which you must pass through to get to Chessboard Land, there is a bottle bearing a label saying 'Drink Me' which, unlike in the Alice stories, will kill you instantaneously then bring you back to life. The setting and characters of the former can be linked to the second Alice installment, whereas the item mentioned in the latter is attributed to the first.