Shelf life of commercial jams with no preservatives

Generally... not as quickly. The salt content of the wine is much higher than drinking wine, which will preserve it longer. It will still "go bad" eventually. (Going bad is more a decrease in quality. It will still be edible, but unpleasant. It won't make you sick, except by the bad taste!)

See this from a Wikipedia Article: "Cooking wine typically available in North America is treated with salt as a preservative and food coloring."

So, it's safer than normal wine, but I'd try and use it soon. The sooner, the better.

On the contrary, most of the older recipes that I've seen for jams use more sugar (60g per 100g or higher is common) than is popular in some of the newer products, because sugar has a preservative effect. But most likely pre-refrigeration and pre-iceboxes you simply wouldn't have kept multiple jars open at the same time; you'd use one at a time as quickly as practical, and keep your reserve stock seals unbroken.

Industrially refined pectin has actually reduced the amount of sugar necessary to make a good preserve. A number of companies also now make "all fruit" spreads, but they're controlling the sugar ratio with knowledge from food science, by analyzing how much sugar is in the non-primary fruits like grape and apple juice.

60 grams of fruit per 100g or more are available but by traditional standards are quite a luxury, even though I would agree that such products often taste better; they owe their existence to better food science, however, and a little to refrigeration.

A lot of widely-distributed brands still use sugar ratios that are pretty high, including Welch's and Smucker's, but you may find higher fruit ratios in boutique brands.