Were any other turn based strategy games invented for the same purpose as chess? Why did chess become so dominant as opposed to the others?

there are a number of such games. Chess evolved, possibly from India, into Chinese chess, Japanese (Shogi), Burmese, Thai and some others. The Chinese version seems more realistic with cannons, a river (which limits who can cross) and a fortress (with special rules) for the King. Burmese is real interesting, it has more resemblance to European with a promotion line (diagonal). It also has an interesting elephant with the same move as Silver General in Shogi. Shogi is rather more positional and slower, Chinese is very tactical and develops quickly.

The pettia family of games is also warlike in nature, often has asymmetrical forces/goals; but with only two types of pieces, the pawns and a King. Capturing is by means of "handcuff capture" totally different than most other games. A good example is the Viking game of Hneftafl where one side has a King who needs to escape; the other side surrounds them and tries to capture the K and his protectors. But there are many other examples: Seega from North Africa possibly 2000 years old; Lundus Luntruculum from the Roman empire, etc. R.C. Bell describes another version where the original rule set was lost and he tries to recreate the game.

The alquerque family of games is also very old maybe 500 years. You have may have seen. Like fox and geese and games like that. Tigers and sheep etc. You try to either capture the fox (or tiger) or else the fox or tigers (typically 3) try to escape. It's not very warlike but a little and its asymetrical.

Jungle chess is sort of like Stratego but you can see all the pieces all the time. it is a more of an invented (rather than a traditional) game about 100 years ago. There are several traps and a home base you need to move into. The pieces are various animals. THe shape of the board suggests that Stratego used this as inspiration. It is a VERY GOOD game, it's not a childs game at all, it has interesting strategy.

The Siege of Paris is another game that was inspired by the Franco Prussian war and is probably a hundred years old. It is another invented game and is similar to captures in Alquerque with some additional rules.

There are a few others that were inspired by WW I and WW II. Most of them having to do with different units with different captures and different movements. You can find them on Boardgamegeek.com

a good starting point, that explains all these games is: R.C. Bell Board Games of Many Civilizations. it is open to some criticism that it does not explain every game correctly (the above games are covered quite well, but there are lots of other games here) but you have to understand he was working many years ago, and did very well to collect accounts from many different regions.

As for the popularity of chess. Of course it is a very good game, only Go surpasses it in terms of depth, while the other versions of chess are similar in terms of depth. Hneftafl and the pettia family are probably not as deep but still pretty deep. Alquerque and Jungle chess perhaps a little less so.

Not only the depth but chess also has more of a narrative feel than Go. In Go every piece is the same, and the concept of grabbing territory is more abstract than the visceral element of killing (capturing) the King. CHess has knight dashing in among checkered squares of infantry, Bishops shooting from odd angles, rook or chariots are powerful but lumbering. You have noble sacrifices, you have faceless pawns that do the dirty work, you have outflanking and powerful head on attacks.

Also it should be mentioned that chess was institutionalized at several times in its European history. In the old days, guys who knew how to play could entertain people on street corners by playing simultaneous or playing with handicaps You could probably earn some money this way. By the late 19th century there was a European tour that wandered from city to city like a vaudeville act. With announcers conveying the information to spectators: "Oh look Janowski has entered into a speculative sacrifice, can Marco hold him off? "Will Lasker grind out an endgame vs Tarrasch or can the doctor's Bishop save the game?" "A daring Kings gambi; a deep positional game, a brave and risky Dutch defense."

Also, it has been institutionalized at various times. Iin the 1930s the Russians sort of used chess as an opiate for the masses. It is easy to teach, cheap materials and provides endless fascination to fans. So they started schools, clubs, promoted the stars and gave the people something to be proud of. Similar stuff has happened in different times in different places; ESPN once carried Kasparov/deep blue, american schools often have teams, the Univ of Md -Baltimore has sort of created its own institution at college level.

So that's maybe some ideas as to why chess has endured. It does have more of a narrative or dramatic feel than Go; both of them are so deep that mere mortals are always thrilled by the unexpected combos.