@Bored-chan (It's a month late reply since I let chapters pile up so I can binge read.)
IIrc, the "accomplisments", tasks beyond ordinary duties, help him get promoted more quickly.
The higher his rank, the more access he has to dungeons. This allows him to improve his powers faster. The more powerful he is, the easier to get promoted.
Of course, the higher his rank, the more privileges he has... like playing his beloved games. Priorities, heh.