To put it another way, if losing £100 is infinitely bad, then you'd never engage in any risk, no matter how small, which had any chance of leading to such a result. This means, in essence, you'd never do anything at all.
I disagree that every action has a chance of losing everything you own. Nevertheless, we're not talking about real life, we're talking abstractly - you were asking about the game theory perspective. Game theory doesn't assign values to outcomes, it just gives results based on the values you assume. You can assume any values you like. If you assume the value of money is logarithmic, there is a definite difference between risks and gains, therefore they are not the same from a game theoretic point of view. From the point of view of a given value system, they might be equivalent or they might not, but that's part of the value system, not of game theory.
For a more realistic value system that displays the same behaviour, assume there is a certain amount of money you need to live (to buy food, for example). If you have less than that, you die, if you have more than that, you get a few luxuries. It's is reasonable to assert that no amount of luxuries is worth death (plenty of people would disagree, but it's still reasonable). (This is similar to the advice given to casino goers of keeping their taxi fare home in a different pocket to their gambling money - however sure you are of a bet, it's not worth risking not being able to get home.)