For Log Horizon, the stakes aren't quite death of course, but they're still something. A lot of it is a loss of freedom. Just look at when they Spoiler went to take the druid girl from Demigas' guild that's holding an entire city to their will. If it went wrong, she would have stayed captive and been treated awfully. Or again, look at when what'sherface blue wolf girl tried to ruin their city's prosperity through using the people of the land. If they failed there, the city would have become far less than it was. So there are stakes, but just because they're not death doesn't mean they're nothing.