在本句中，that是程度副词，用法等于so。

Life isn't that much of a damn contest to us.=

Life isn't so much of a damn contest to us.

又如：

When you pay that much for a meal you expect the best. 一顿饭花那么多钱是想吃到最好的东西。

The bridge can't hold that much weight. 那座桥不能负载那样的重量。

And no, I haven't given it that much thought yet. 但我还没怎么想这件事呢。

I don't have that much money on me. 我身上没带那么多钱。