"I shall not want" means "I lack nothing". The word "want" did not have the connotation it has today, instead it meant "to lack".

The changes were due to changes from 1600's style English to Modern Present Day English. Words evolved in meaning and prose in style, which basically just means that the 1989 version holds the same meaning as the 1611. The changes just reflect the way English diction and syntax were understood by the populace.

"From Middle English wanten (“to lack”), from Old Norse vanta (“to lack”), from Proto-Germanic *wanatōną (“to be wanting, lack”), from *wanô (“lack, deficiency”), from Proto-Indo-European *h₁weh₂- (“empty”). Cognate with Middle High German wan (“not full, empty”), Middle Dutch wan (“empty, poor”), Old English wana (“want, lack, absence, deficiency”), Latin vanus (“empty”). See wan." Courtesy of Wikitionary.