There are indeed some influences from post-rock noticeable on some of these songs. However, if my knowledge of musical history is correct, post-rock evolved from shoegaze and slowcore, which makes a better description for this music. These are mostly slow pop songs with a great sense of melancholy, reminding me of bands like Low, Codeine, Red House Painters and at times even South San Gabriel meets Slint.
In a way, you can see most of the songs on 'This Is How We Fail' as folkish singer/songwriter tracks, enhanced with a full band. Songs like 'Out Of Tune', 'Break' or 'California' are quite minimal pieces of music, without too much technicality, which keeps the whole thing down-to-earth and intimate. Here and there you can hear a flash of grunge, like in my favorite track 'Worker Bees', a song that has something cabarettesque.
In all, 'This Is How We Fail' is an excellent alternative pop rock album, one in a genre you don't encounter that much these days. If you're a nostalgic person, longing for some nineties melancholica, this definitely is your thing. The level of songwriting is excellent, there's enough variation and there are some beautiful tunes to be discovered here. So check it out, you won't be disappointed.