You're right about chess having a timer, although you tend to get 2 hours for 40 turns (3 minutes per turn), unless it's speed chess, which isn't the same kind of pressure as completing the whole game in 25s! However, this is what game jams are all about, trying out new things to see how to do them and what people think of them. We had 2 stacked timers in our last game jam, a flare for light which ran out in 5 minutes and an oxygen tank when swimming underwater which lasted another 5 minutes. Some people liked the jeopardy of them, but others did not. We had one of the original team who worked on Command & Conquer and Eye of the Beholder games review our entry, and he had some strong opinions on timers that we took on board.
We learn so much every time we do a game jam. It really is valuable, and the time pressure sparks the creative process in a way that you just don't get outside of a jam. Knowing that you have an audience for your game at the end of a jam, and that you're going to get feedback, makes all the difference. Well done again for completing your game and best of luck with your next one. Each one gets better in our experience.