Number of possible outcomes in Bernoulli Dice Game

Question

To illustrate the issue of skewed distributions, we consider a solitary game where:

1. A player rolls one dice, securing a result $i$ ($i$=1,2,..,6)
2. Then selects $i$ dices out of a set of 6 dices and throws them once, obtaining a sum $s_i$

If the sum $s_i$ is:

• $s_i>12$, the player gets one unit payment
• $s_i=12$, it's a tie
• $s_i<12$, the player pays one unit payment

The total number of outcomes is supposedly $6*6^6$ [From Epstein's Book]

My understanding would be that the number of outcomes is $\sum_{1}^{6}{6^k}$ reflecting that for the case with one dice you get $6$ outcomes only. Is the author considering all 6 dices as different outcomes of the first roll (meaning that getting $i=1$ and picking dice 1 or 5 is different)? If so, why is that?