Because pool refers to any type of pool, not just swimming pools. They showed a picture of a swimming pool because a swimming pool a type of pool, but that does not mean that pool only refers to swimming pools.
Translating pool ("pool") as "swimming pool" would be analogous to translating färg ("color") as "blue."
According to the Folkets Lexikon, pool may refer to billiards, a common fund, or basins or swimming pools. I do not know if pool it can be used to refer to a small, shallow patch of liquid lying on a surface (one of the New Oxford American Dictionary's definitions), such as a pool of blood, or a figurative pool of light. I may be wrong, but it seems from the Folkets Lexikon that pöl would be used in that case (don't take my word for it).
I did some Internet research. It turns out that that "weird reason" is one that has to do with the history of the game. Originally, the game was called "billiards," a name it continues to bear to this day. The word "billiards" comes from French—either from billart which is one of the sticks, or from bille, which means "ball." Although the game's roots are in 15th century Northern Europe, 15-ball billiards as we know it today was developed in America at the end of the 19th century or the beginning of the 20th century. The tables were installed in houses where bets—or pools—on horses were made. This would give the gamblers something to do between races. For this reason, the houses gradually became known as "pool houses," and with time, "pool" began to be used to refer not to the betting pool, but to the game.
I can't find any confirmation of this online, but I presume that pool, at least when used in this sense, is derived from the English by way of the Americans. I looked at the Swedish Academy's Wordbook (http://www.saob.se/artikel/?show=poolunik=P_1433-0117.J8dApz=3). I can neither read the Swedish nor decipher the abbreviations that they use, but I see "eng." in there, which possibly stands for "English."
'A swimming pool' has since been added as an accepted answer. en pool in Swedish very often refers to this kind of pool, so that with no context, it actually makes sense to assume that 'a swimming pool' is what is meant (more sense than it would the other way around).
The word is also used about things like 'a car pool' or about staff: skolans pool av vikarier 'the school's pool of temps' and in sports, about a group of teams. It is not used in the "small patch of liquid" sense that HPFoley mentions, that is indeed en pöl (for 'a pool of light', I'd probably use some other word instead), and the game 'pool' is biljard.
Other word for 'a swimming pool' in Swedish include en swimmingpool, en simbassäng, en bassäng, en badbassäng, so that the main answer should probably still be just a pool.