I do agree that serious applications moving towards a more cartoonish feel is not a good design trend.
However, in this case I can't agree as I don't think anything you pointed out is over-done. The font comes close, but it isn't used for every single word, just for emphasis on certain words.
Re:Show HN: Quire – Tasks done right
by tmillsclare on Wednesday April 29, 2015 @12:51PM
(#9459655)
Thanks for the feedback both of you. Our design was intentionally kept a bit light-hearted while trying to maintain professionalism.
We do think this strikes a good balance.
I really hate anime and it seems to be coming more pervasive in the web design world.
I think you should reconsider the images and the font as it doesn't make your application look professional whatsoever. It isn't advisable when you are trying to advertise that your task management application makes people's lives more organised...