Should Victory Points have Meaning?

Personally, I like to think of Victory Points as a measure of success, regardless of the theme or environment of the "game-space." The more you have, the "better" you are doing in the game. Most of the time, the goal is to do better than all the other players, in which case you become the winner.

Should VP have meaning? I suppose your intent was something like whether or not VP should have some sort of thematic connection. An obvious, easy answer would be "Yes, of course!" However, you'll find exceptions to this principle, whether it's a abstract game, a long or short game, a card game or board game, or whatever.

If your game works without an obvious thematic connection to the VP, then you don't necessarily need to tack it on. Like in Settlers of Catan, which is downright infamous, you don't necessarily need to have meaning behind the points themselves, other than the fact they are a reward/incentive for performing specific actions. In other words, if you (as the designer) want players to do certain things in the game, then reward them for doing so. VP are but one form of reward. I perceive this as basic positive reinforcement.

Can VP be considered a resource? Certainly. Why not? Personally, I also like the idea of VP as currency in certain situations. As long as the option is worth considering at some point - providing proportional gain for the risk - then it could significantly add to the game.

Generally, relinquishing VP can be seen as an always-sub-optimal move, but it doesn't have to be. Depending on the timing, it can be beneficial. The interesting choice for the player can be, "Is it worth moving myself away from winning by spending my precious Victory Points in this transaction? What are my chances that taking a step back now benefit me later - but not too late?"

If you want to think about it in a more general way, you can approach it from the perspective that since all games are about reaching a goal, that goal has to be quantifiable. This could be the quantity of anything, like health points reaching zero, having the highest vp when the "time tracker" reaches 10, or anything else that can be counted becoming specific value (number of players, king figures in a specific position, cards in hand, anything!)

Victory points are usually used when we want to quantify something that you usually can't, like who made the best art, who is the greatest leader and other more vague and hard to define things. For instance, you could define the greatest city by the on that has the most buildings, but once you say that how many people does it have or how much money it makes also matters, you have to weight those values against each other (so you can compare if the city with 5 buildings and 10 people or the one with 3 buildings and 20 people is greater), so you assign a weight to each of those values, that's where it helps to have a combined value (so city 1 is 5*3+10*1=25 and city 2 is 3*3+20*1=29 greatness points). So VP's are great for measuring abstract things or when several measures have to be combined!

Answering the actual question (sorry for the lengthy write), VP's are good when you want to measure abstract things (like greatest civilization, best vampire), so if your thematic requires an abstract end goal, you can use VP's for it (calling it best vampire or culture points), but since it is an abstraction in itself, you can keep it abstract, it's a question of your thematic taste and if you feel the game requires that heavy thematics or not.

Have a great day and best of luck!

Of course they should. (And there will be concrete advice after the following paragraph).

I think of them as the great semi-definable concept in economics, utility. Effectively you're trying to come up with a quantifiable value that takes in a large number of mushy (not the formal term) factors.

So to find an answer to the question, "How should VP be meaningful in my game design and how do I assign them accordingly?" look to your theme. What defines victory not for the player, but for the role the player is taking.

Example: (pre- or low industrial) empire building games. Think about who is the best shape to survive x years (or y turns) after the game's end. If a player accumulates giant armies, so many that the VP formulas yield victory, but the empire has no food, no money to trade for food, no means to conquer food within a few turns, the victory, the design should feel hollow, regardless of brilliant innovations, art, miniatures, and glowing reviews.

Example 2: Boxing. Win lose draw. Let's throw out draw. If your players are taking the roles of fighters at the beginning of their careers, consider how a serious concussion might be worse than a loss. Or if your style is not terribly engaging, you need something else to get that big payday. (Not everyone can be Lennox Lewis, who took his chess quite seriously)
Late career? Last fight? Your brain is mush anyway, let the refs scorecards say it all. Get the big payday, spend it on drugs and private medical care.

Hope this helps.
Hop.

Without "meaning" (which I presume means connection to the model you've created), you have a "points salad" game, where there's no obvious reason for the VP other than the designer made it work somehow. Points salad is almost as bad as mechanics salad in my book. YMMV

Yes, VP should definitely have meaning and be directly related to the game. But see if there's actually a better way to illustrate the relative performances of each player. I mean, imagine Chess with Victory Points...