Spiral Knights (SK) was designed as a Player-vs-Monster/Enemy game (PvE). Two Player-vs-Player games were shoehorned in as an afterthought, but the mechanics of the game really weren’t meant for PvP game play.
SK is a completely Free-to-Play (F2P) game. Every part of the game and every item in the game can be gotten for free. Player can choose to spend money for additional energy or promotional items, but these items can also be obtained for free through the in-game economy. If you are really into the game and spending real world money on the game brings you more enjoyment, then by all means do it. Three Rings is certainly hoping that will be the case since their business model is based on just that.
Nothing in the game is truly Over Powered (OP) and the game play is challenging without being overwhelmingly difficult. For very good players, even the game can even be too easy. There is no “Win” in SK. You play and have fun and the normal 5* gear is enough to allow you to complete everything in the game.
Some players accuse SK of having become Pay-to-Win (P2W). P2W can be defined as . “a game where players who are willing to pay for special items or downloadable content may be able to gain a significant advantage over those playing for free.” (Wikipedia) Since the game is cooperative rather than competitive, the concept of an advantage does not exist, except to the limited group of players dedicated to Lockdown. Another definition of P2W from Urban Dictionary is “Games that let you buy better gear or allow you to make better items then everyone else at a faster rate and then makes the game largely unbalanced even for people who have skill in the game without paying.”
P2W cannot be applied to SK since we are not competing against one another. It’s really rather the reverse. We form parties and guilds to play together. If a player wants to buy the 5* gear right away, it only benefits other players. Even though you can obtain the highest level gear instantly, it certainly does not unbalance the game or give players any significant advantage to do so.
This game is primarily PvE, not PvP, nor is it P2W in any true sense of the term.
As you have mentioned, the term "pay to win" isn't really a concrete term, and can mean a large variety of things. If anything, I think that "pay to win" deserves more of a sliding scale than the yes/no model people tend to give it.
In our case, players cannot just pay and win, nor do players have to pay to win with the addendum of certain content requiring someone somewhere to make a cash purchase for energy or otherwise. The flip side to this being that players who put money into the game receive what is basically power over other players, the environment, the economy... a perceived unfair advantage over others with regards to acquiring the best loot and having the nicest chances. Regardless of how you or I decide to brand the game, this is the basic underlying truth of the matter and it happens to be one that many people don't seem to be comfortable with.