Technically, I think it's not that instrumental goals tend to converge, but rather that there are instrumental goals which are common to many terminal goals, which are the so-called "convergent instrumental goals".
Some of these goals are ones which we really would rather a misaligned super-intelligent agent not to have. For example:
You can't take an empirical approach to existential risk as you don't get the opportunity to learn from your mistakes. You have to prospectively reason about it and plan for it.
As the pre-amble to the statement says: they kept the statement limited and succinct as there may be disagreement between the signatories about the exact nature of the risk and what to do about it.
The emergence of something significantly more intelligent than us whose goal are not perfectly aligned with ours poses a pretty clear existential risk. See, for example, the thousands of species made extinct by humans.