I've got a couple that I don't see on the list, and which don't have any kind of website associated with them I can find. I discovered them through TVTropes, and they seem to be somewhat known about as free games, so I'm not sure whether or not they should be added. Also, they are Japanese in origin, though being relatively straightforward puzzle games this does not affect gameplay much. The games in question are
Ai to Yuuki to Kashiwamochi and
Irisu Syndrome, by the same creator (sorry for the links). They are both very difficult puzzle/horror games, which I guess would go under 'strategy'? High points are music, addictiveness of gameplay, especially for the former, and very effective use of meta/interface related horror. Low points are somewhat odd graphics and slight bugginess, most likely due to how old they are. Difficulty could be a plus or a minus, depending on the player.
There are also a couple of other games, mostly Japanese again though most have been translated:
Yume Nikki ('Dream Diary';
Home page and [img=http://www.theneitherworld.com/yumenikki/index.htm]http://English fansite with translations and such[/img]), a horror/adventure game made with RPGmaker, with a tight focus on exploration.
This one's pretty well known, I was surprised not to see it here. The idea behind the game is that you, the character Madotsuki, are unwilling/unable to leave your apartment and so spend most of your time exploring the world of your dreams. The horror in the game is mostly very surreal and fairly low key, though several fangames have been made (most linked to on the english website above. I particularly recommend .flow.) which increase the horror levels. Not a very exciting game, but the environments are spectacular in all respects. The music, while minimalistic, is likewise very well done. The main downside to this game is that when all is said and done, there is relatively little to actually do, and walking through the same areas to get to wherever you're trying to go can get tedious. On a more subjective note, as there is only one character and no opportunity for exposition, it is entirely up to the player how they want to interpret Madotsuki's life and dreams.
Ib (
Home page and
English fansite), another horror/adventure game made with RPGmaker. Much more recent, more straightforward, and only slightly less surreal, though more horrifying.
This game follows the title character, a young girl, and a few others who are stuck in a strange art gallery as they try to find their way out. Like Yume Nikki the horror is mostly more surreal than it is threatening, though unlike Yume Nikki it is actually possible to lose. Also, there is more of a focus on character interaction, given that there are actually multiple characters. Not difficult, but not pointlessly easy. The puzzles are mostly engaging, and apart from a few chases there isn't much required in the way of reflexes. Again, high points include visual design and music. The characters are fairly well developed, considering the game's length, and the story, while nothing spectacular, is interesting enough to keep you playing. Bad points are awkward controls in some areas, some technical glitches that might arise at a few key points in the game, and some purely luck-based puzzles which can be annoying. Also, installation can be confusing.
There's also the rest of the Chzo mythos, but it should be easy enough to find them through 5 days. Sorry if I was too wordy.