As long as you use sterilized jars and make sure they seal, these should be able to be stored in the pantry. For safety's sake, if you concerned about homecanned goods, you could alter the recipe slightly by packing the raw pineapple into sterilized jars, heating the other ingredients to boiling, pour them over the pineapple, putting on the lids and processing in a waterbath for a few minutes (approximately 5-6 minutes should do). Though you could do it this way, the recipe, as stated should be safe. First of all you are using vinegar to help preserve, and pineapple is also very acidic so safety should not really be an issue. Any jars that don't seal should go into the fridge ASAP, and eaten soon, but the others should stand up to storage in a pantry, and would probably benefit from some time maturing, as all pickles do.