While I haven’t consciously adopted a "philosophy" of design, these are my observations of what happens.
I design two kinds of games. One kind is strategic, I hope with some gameplay depth, and highly interactive (like Britannia or Dragon Rage). The other kind is "screwage" games (where you "mess with" the other players) that are not very strategic, but provide a fair bit of interaction within the game (though this varies)(like Sea Kings.). I am no longer a big fan of two player games, and even when I design something that is two player, I try to provide for partners play.
The strategic games tend to be 2-3 hours long, the screwage games under an hour. Some of those games can be played quite quickly, but I don't design games that are intended to be less than half an hour, because such are bagatelles ("a thing regarded as too unimportant or easy to be worth much consideration".).
I prefer fairly simple-to-play games over fiddly, rules-complex, or many-pieces games. I avoid any deliberately-added complexity. My motto is "A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away." - Antoine de Saint-Exupery. Another form, about Japanese gardening actually, is "Your garden is not complete until there is nothing else that you can remove."
I dislike puzzles, things that have always-correct solutions. Like most Eurogames (not all) and most single-player video games (not all).
I try to keep the number of pieces, cards, and other Stuff a player controls to under two dozen in multi-player (more than two players) games, and under three dozen in two-player games. Strategic and tactical complexity can be achieved without large numbers of elements to keep track of.
On the other hand, I am not of the "I only want a few alternative choices" school. In other words, a chess-like element is often in my games (lots of different possibilities, though few pieces). I have simplified some of my games (generally the screwage card games) to the point that only a few practical moves need to be considered each turn.
Part of the "chess-like" method is that you must watch every move your opponent(s) make, and react to it. (Though the reaction can be to ignore it, you have to figure that out, not ignore it to begin with.) If you don't "watch like a hawk", you are very likely to lose.
I try to reduce the effects of chance in strategic games, either with lots of die rolls that will tend to "even out" (Britannia) or by using elements such as cards that players have some control over. The more cards are used in a board game, the less dice should play a part.
I design games, not simulations. I prefer players to have control of their pieces; perhaps they can’t do everything that they want to (that’s good, it makes them make choices), but there is no random element that prevents them from doing something with their pieces, however realistic that may be. In the end, it’s a game. Hence, I have little interest in many of the more recent additions to wargames that model the huge uncertainty of warfare such as "chit pulls", activations, and "card driven".
I like the game to represent something, to be a model. In many Euro-style games, the atmosphere (often wrongly called theme in this case) is "tacked on" (and could be changed considerably), and the players are entirely concerned with pure mechanics and with the other players. I like to be able to understand that when I move something in the game, or do something in the game, it’s something like an event that could happen in reality. And when something happens in a game, it could have happened in reality. Having been educated in history, I am far more skeptical than most about relating real-world events to game events.
An historical game can teach the players something about history. I am not, however, of the "what if" school of varying one factor or one decision to "see what would have happened". My games tend to be at a high (strategic) level where it is practically impossible to "model" the factors that produced history, so it is rarely practical to use the "what if" query.
So I model effects, not causes.
Despite all that, I do design the occasional fairly abstract game, because abstract games are a form of "pure" game. What I rarely do is design an abstract game but pretend it's something else.
People play games for many reasons. I play either (in cooperative games such as D&D) to "succeed in the mission" and keep everyone on my side "whole", or (in competitive games) to win the game. I like to know the rules of a game thoroughly; I much prefer to read a set of rules rather than have someone teach me, probably because I want to thoroughly know what’s going on. I recognize that the rules-reading preference, in particular, is a minority view! Nonetheless, I tend to design games that I like to play, though I design games for other people, not for myself.