Etymonline has this to say:
c.1300, replacing Old English wingeard, from vine + yard (n.1). Compare German weingarten.
If it is a compound of vine and yard there would be little reason to shorten the i of vine. However, I can see two reasons why it would have shortened.
The first would be that the "replacement" was really just a spelling change, and teh word never was seen as really different from wingeard, which I can imagine to be pronounced in a similar way as teh modern pronunciation of vineyard (at the very least with a short [i]).
A second one, but this is mere speculation, is that longer vowels tend to get shortened in compounds over time. Many place names that where formed as town became ton.
I would assume it is pronounced in a similar way to wingeard, since that is the actual word, even though someone decided to change the spelling to make it look like a compound that it may never actually have been. If you wonder how this could be possible, look up the history of the word colonel!