You've hit my hobby (but I dislike the games you're talking about).
I'd contend chess's outcome is based purely on the decisions of the players, but there are often close calls in that game as well, which it is reasonable your opponent will zig or zag, etc, where your chances of winning come up entirely on if you happened to believe if he was zigging or zagging and did moves to counter zigging or zagging appropriately several turns ago.
Multi-player games still have the chaos of multiple people making decisions. So yes, there is no technical randomness, there is still chaos and uncertainty:
Lifeboats: http://boardgamegeek.com/boardgame/249/lifeboats http://boardgamegeek.com/boardgame/483/diplomacy Stratego: http://boardgamegeek.com/boardgame/1917/stratego Blokus: Lay down tiles and try to last as long as possible
http://boardgamegeek.com/boardgame/2453/blokus
Gemblo: Same as blokus, harder to find in the US, done better: http://boardgamegeek.com/boardgame/19427/gemblo
Antike: http://boardgamegeek.com/boardgame/19600/antike only luck is who you get as your place on the board. It's okay, but it has a certain snowball quality to play some games. Somewhat Risk like
Hive: http://boardgamegeek.com/boardgame/2655/hive chess, without a board, with bugs. Fun, short, but non-random
1830: http://boardgamegeek.com/boardgame/421/1830-railways-robber-... a game about being a robber baron. Interesting stock market mechanic, etc.
Of these, lifeboats is a little fun, but honestly, most interesting game mechanics are there to make a game playable more than a few times (which is one thing the above games lack), and most of them have some degree of randomness. The next crop of games has a minimal random element:
Power Grid (Random element: which power plants will be up for auction): You all play Monte Burns esque robber barons over a electrification empire. Very "brain burner" to many people's minds: http://boardgamegeek.com/boardgame/2651/power-grid
Puerto Rico (Random Element: which plantations are available this round): You play plantation owners on Puerto Rico during the days of the sugar trade. The theme is distasteful to some http://boardgamegeek.com/boardgame/3076/puerto-rico
Chicago Express (Random Element: Seating order): Robber baron type scenario, but playtime is http://boardgamegeek.com/boardgame/31730/chicago-express