I could be wrong so someone please verify this but I believe Space Empires: 4X does not have a set amount of turns. I own it but have yet to get it to the table and it's been a bit since I read the rules. This is primarily a two player game though.
…Is there a game like Twilight Imperium 3rd edition, that is shorter…
One thing I will mention here is the 4 player rules for TI3 have each player pick two strategy cards per turn which for our group cut the time down to closer to 3 to 3-1/2 hours. Sill long but less then half our typical TI3 play with 5 or 6 players.