Good question. While both מחרתיים and ביומיים can be translated as "in two days", there is a difference between them. מחרתיים talks about a point in time and ביומיים talks about duration.
Here we have מחרתיים which means "in two days" as in "the day after tomorrow" - מחר is tomorrow and מחרתיים is like the dual of tomorrow. אני אשלח לך אותו מחרתיים. I will send it to you in two days.
And ביומיים also means "in two days", but in the sense that something takes "two days" - something like "within/during/for two days". קראתי את הספר שלו ביומיים. I read his book in two days.