Windows 8 Machines Only Have Primary Partitions?

Solution 1:

Well, we've come a long way since the FAT file system. These days, there are two disk partition styles with Microsoft:
1. The older Master Boot Record (MBR)
2. GUID Partition Table (GPT).
MBR has the limitation of allocating only 4 primary partitions, but the newer GPT can support upto 128 primary partitions. And it is recommended for large HDDs.
Newer computers have newer BIOSes named Extensible Firmware Interface (EFI). They can use the GPT partition scheme.

Your laptop supports EFI, and it has been configured to a GPT disk, so get on with multiple primary partitions. :D

Solution 2:

The 4 primary partitions limitation is because of the old BIOS.

It seems your new laptop uses UEFI which supports more than 4 primary partitions.