Vinegar is handy to have around, its cheap, and I don't think it ever goes bad.
^ This
Unsweetened, unflavored vinegar won't ever go "bad", though ones with distinctive flavors will fade over time. (But we're talking
really long time periods here. Years. Not months.) Mass-market "balsamic vinegar" may gunk-up/settle to the bottom if unused for months at a time, but the worst offenders are also cheap, so easily replaceable. I can't really imagine not having at least distilled white and white wine vinegar around, plus, preferably, rice vinegar, though the wine vinegar can be slightly diluted with water to stand in for the latter, and filtered cider vinegar isn't a terrible substitute for wine vinegar. Though again, if shelf life rather than storage space is the issue, I see no particular reason to stint on any of them since they're relatively inexpensive and have such a long shelf life.
Oil, especially olive oil, on the other hand, has a comparatively short shelf life at room temperature, so I would buy that in small bottles, and keep it in the fridge, or at least stick it in the fridge before I left to go traveling. (Or keep the larger bottle in the fridge, and a small one on the counter.) Some veg oils (safflower, grapeseed, etc) have a somewhat longer-than-average warm-room-temp shelf life, but none of them lasts forever. (I've found that many people seem not to notice that their oil went rancid months beforehand and keep it using long past the point where I'd feed it to a starving rat... I think that's gross, and it's not healthy, though it's also not acutely toxic.)
As for the rest of the OP's list, I'd add at least a few things:
Salt
Pepper (specifically, whole peppercorns)
Olive Oil
Flour (roux)
Cornstarch
Garlic
Onions
Ginger
Soy Sauce?
Hot sauce (e.g., Tabasco)
Worcestershire sauce
"Wine for cooking" (but the not the stuff sold in supermarkets labeled "cooking wine")
Stock Powders
Canned broth
Canned beans
Spices/herbs
[...]
Maybecanned tomatoes (and tomato paste).
In the past I never carried flour but I've recently discovered roux and now
Is vinegar necessary? Yes A bag of sugar? Yes
Dry pasta
It depends to a large extent where the OP lives and what access there is to groceries. I can, for example, easily buy quite a wider selection of things than are on the OP's shortlist 24/7 within a few blocks of my apartment, at a 24 hour "drugstore" like Rite Aid or a small corner convenience store. I might overpay for some of them at 3am, but if I want sugar or flour at 3am, I'm not going to to worry about paying an extra dollar or 2 for it...
I couldn't cook happily on a regular basis without soy sauce (and like to have SE Asian fish sauce on hand too), but its "necessity" depends on what the OP cooks. It keeps well quite a while at room temperature, and a
very long time in the fridge.
I also consider tomatoes a food group in their own right

, so at least a small stock of my preferred brands (not available in my immediate neighborhood) would be a must. (As it is, I've managed to amass enough to keep half the population of Italy south of Naples in red sauce through a particularly protracted Nuclear Winter.^_^) I'd also keep canned broth on hand. For very small amounts, the powders or pastes are OK, but once you're up to soup-level quantities, they mostly just taste incredibly salty and the "flavor" seems incredibly fake to me... I'd add a couple of cans of a few sorts of canned beans (in my case, chickpeas, pink, and black) as well.
I could probably live without flour for most everyday cooking (I tend to use cornstarch for quick, small-scale thickening), but on the other hand, white (vs whole wheat) flour has a
very long shelf life if kept in an airtight container away from sun/direct light and it's cheap, so I see no downside to keeping a couple of pounds lying around. Similarly, cornstarch basically never goes bad, so I would add a small container of that to the list. And even if the OP never bakes anything, I can't imagine not having at least a pound of sugar on hand for cooking purposes, and more than that, unless the OP uses artificial sweeteners in beverages. And since white sugar will basically
never go even stale much less "bad", there's no downside to keeping it around in whatever quantity storage space allows...
I don't know if the OP considers it a different category of pantry staples he hasn't mentioned, but given the way I cook/eat, the absence of dry pasta from the list shocks me. For quick meals or if push comes to shove, it can be the bulk of a "meal" all by itself, at least with a sauce a little more nutritious/flavorful than basic tomato sauce (and lots of pasta sauces freeze very well.) I normally keep quite a bit/variety around, but I'd want at least one sort of long (spaghetti/linguine/fettucine) and one of short, cut (ziti/penne/rigatoni) pasta available at all times, and preferably some egg noodles, too. It doesn't have a literally
indefinite shelf, but it lasts a very long time even in the original cardboard carton/thin cellophane bag (and even longer if you put it in an airtight, moth-proof canister or larger freezer bags.) For that matter, I can't imagine not having rice around, either, and again, basic white, long-grain rices keeps a long time on the shelf. (Medium/short-grain Asian rices have a shorter shelf life, and brown rice, shorter still.)
I'd also add at least one sort of basic hot sauce (eg, Tabasco), a small bottle of Worcestireshire sauce, and some sort of "wine" for cooking purposes. I know some people who purport to be able to distinguish good food from bad are satisfied with ordinary table wine left sitting in the fridge for weeks/months/years on end, but frankly, I find that incomprehensible. On the other hand, fortified wines with at least 17% ABV like (Julia Child's old favorite-for-the-purpose) dry white vermouth (readily available in half-bottles, with screw tops), or a somewhat heavier sherry (fino ≠ a great choice), will keep well for a fairly long time (6 months) at room temperature and again, a
very long time in the fridge after being opened.
I'd also add a fairly long list of spices/dried herbs, but that's a very personal thing. My bare minimum would include bay leaves, thyme, oregano and/or marjoram, generic curry powder, ground cumin, ground cinnamon, (sweet) paprika, and cayenne pepper. Ground black pepper doesn't have much of a shelf-life at all (and it's not something I'd ever buy in the first place), but whole peppercorns hold up well a
very long time even by exacting standards and even the cheapest pepper mills are fine for occasional use.
As for seasoning vegetables, onions are a poor candidate for long-term indoor storage (excluding those modern rarities - "cold cellars" and pantries.) I would not plan to keep any particular onion(s) around longer than a couple of weeks. Garlic keeps a bit longer (and doesn't stink to high heaven when it rots), but at typical US room temperature, it too has a relatively limited lifespan (a few weeks, maybe) before it (usually) dries out to a husk or (occasionally) rots. Ginger on the other hand lasts a long time in the fridge if only loosely wrapped, and can be frozen, and grated while still frozen. Even fresh herbs that have a short fridge-life (parsley, dill, basil, coriander) but that are really nice to have on hand can be chopped fine/processed/blended and frozen in small cubes/amounts (and are sometimes commercially available in that form.)