This sentence is perfectly acceptable. It is an example of parallelling, where two sentences are combined and the duplicated words are eliminated. The original sentences are
Engineering of applications for the area “Finance and Administration” in IT services, e.g. tools like the payroll app
Responsibility for applications for the area “Finance and Administration” in IT services, e.g. tools like the payroll app
The parallelled version is considerably shorter because the duplicated text (the words that are in bold) is eliminated.
There are alternative approaches, but they generally reduce the strength of the link between the non-parallelled parts (Engineering of and Responsibility for). This may be acceptable if one of them is considered to be more important than the other, but would be a problem if you wanted to give the impression that the two are equally important.
One approach would be to replace the parallelled text in the second sentence with a demonstrative adjective or pronoun.
Engineering of applications for the area “Finance and Administration” in IT services, e.g. tools like the payroll app, and responsibility for these applications.