Macintosh HD partition missing from startup options
The second image you posted shows a partition type of DE94BBA4-06D1-4D40-A16A-BFD50179D6AC. This is for a Windows Recovery Environment type partition.

From Windows, you can open a Command Prompt window as an Administrator. Next, you could enter the commands given below to change disk0s2 to an Hierarchical File System Plus (HFS+) type partition.

diskpart
select disk 0
select partition 2
set id=48465300-0000-11AA-AA11-00306543ECAC override
gpt attributes=0x0000000000000000
exit



  Note: This answer assumes you are not using Core Storage. 


A more comprehensive solution is given as the accepted answer to the question: OS volume shows as type 'FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF'. Despite the fact that your partition type is DE94BBA4-06D1-4D40-A16A-BFD50179D6AC and the linked question partition type is FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF, the accepted answer provides a solution that would work in your case.