Had a talk with the engineering manager. Seemed to have a good conversation and proposed to continue in the process with a talk with HR. Also mentioned my advanced interview stages with other company and the manager appreciated this information, and would try to speed up.
I mailed the manager twice, once the day after, after not getting any contact from HR. No answer. Four days later, I mailed the manager again that I'm getting further with the interviews in another company and if there are some news. No answer. Tried to contact HR and got a generic response in which they "after carefully consideration, they have decided to continue the process with other candidates". No further explanation, no mail at all from the manager commenting anything. Only silence. The company seems quite nice and interesting, but feels like dodging a bullet with this particular manager.