Get clean line-level audio signal from a sound generator chip that is designed to drive a transistor as amplifier
You're looking at the low frequency response of your soundcard input : both the  waviness and the response to a DC step. The flat top squares on your waveform (last plot) are trapezoids in the &quot;other&quot; recording : this just says your recording has better bass response.
If it sounds fine on playback, don't worry about it. If you want poorer bass response, either AC couple into the soundcard, or simpler, use the sound editor facilities to cut the bass. Which is probably all they did on the other recording.