Is reading each part of the Holy Quran by one of the friends within a group sharing the Khatmah (completion of reading the entire Quran), such that all parts are read in a single Khatmah, considered a complete Khatmah for each one of them, even if each one read parts in a non-sequential order?

For a ختمة (complete recitation of the Quran) to be valid, it is not a condition to recite the Quran in the order of the Mus'haf, even though that is preferable.

It is better for each person to complete their own ordered ختمة. Competition in completing recitations is permissible, as is gathering to recite in one of the legislated ways.