Why not 'other violent crime' - it's more directly comparable to rape.
Because failure to prevent other violent crime could also lead to compensation in the same manner as this case. This case says that where someone is subject to torture or inhuman or degrading treatment, there is a duty to effectively investigate and prosecute. The violence has to be bad enough to count - rape clearly is, but other forms of bad violent crime could too.
I can see why they chose fraud because it’s a classic example of non-violent crime. But equally when the response was effectively “Oh dear, we might have to start prioritising rape more instead of fraud”, my thoughts were “Shouldn’t you already be doing this?!” 
Someone else on the thread was worrying that men might use this to get compensation where they have been wrongly accused of rape (or claim to have been...) and don’t think the police investigated properly. I don’t think it could be, because there is no torture/inhumane treatment etc. I’m a lawyer although this isn’t my area of practice.
I can see why the police fought this because it’s been a long-standing principle that you can’t sue the police where they fail to investigate properly (even where they could have stopped a murderer or rapist), but I’m very glad the women won as I think this unfortunately might be the only way to change police priorities.