Sorry, I cannot see the problem. The voice of the first video is clear and there is absolutely nothing that I would change. The background music, ok, hmm, what shall I say. It is, yes, it's some kind of music. If you know, what I mean
But also clear and good quality.
In the second video there are four people talking, very authentic, I don't know, who you are and I don't see, what to make better.
I don't know, with what program you are recording game and voice. But if that program can handle VST plugins in realtime, have a look at the youtube searching machine of "pedalboard 2". There are described kinds of VST "cascades" for pushing audio in realtime. I use it to be able to record voice without the need of working on it later.
For further ideas, sorry, I am not the right man, I am no audio professional.
Hatti
Win 10 64, i7-4790k, 32GB Ram, 256 GB SSD, SATA 2TB, SATA 4TB, NVidia GTX1080 8GB, LG 34" 4K Wide, AOC 24" 1080