As @user13484 pointed out, the general concept of two (or more!) melodies sounding together is counterpoint ("note against note").
The term counterpoint is used when the melodies that are sounding simultaneously are independent and are more or less of equal importance. Both rhythm, pitch but also timbre can be used to achieve independence. The term is about a technique or texture, and as such it may be applied to a section, or a movement or even an entire composition.
"Independence" is not a matter of all or nothing. Although the melodies might have a different rhythm, a melody might have the effect of emphasizing only particular accents of a main melody. Or although a melody might be playing different pitches, it might do so in an identical rhythm. So in those cases, the extra melody is not truly independent.
With regard to this piece, the parts that are entering at 0:15 do not really seem to carry a new or separate melody. The new part serves mainly to give the piece a new rhythmic pulse. The head of the new part serves to accentuate and repeats the same pitch a few times. The tail of the phrase basically mimics the main melody (it's not exactly parallel since the rhythm is slightly different, but the pitches are). So there is a certain lack of independence, and I'd argue the parts also aren't equally important, which is why I would not call this true counterpoint. I'd call this simply "accompaniment".
At 1:30 though, something starts to evolve that does sound like true counterpoint, first in 2 parts, and then at 1:45 in at least three. Here you can clearly here different parts that are independent in movement, curve, rhythm and pitch.