That was definitely the problem. That System partition is necessary for booting, and it's good that you caught this now, because if you had a hard drive failure at some point in the future and tried to restore from a backup that only had your C partition, you wouldn't have been able to boot your restored backup. Those extra partitions aren't there just so the PC gods can arbitrarily take up space on your system.
Fyi, in your screenshot of the whole Reflect interface, do you see that option under Backup Tasks in the upper-left corner called "Create an image of the partition(s) required to backup and restore Windows"? Click that and see which partitions are selected by default. Any system image backups should include at least
those partitions. The rightmost partition on your disk is probably your manufacturer's factory image restore partition, which you may or may not want to bother backing up depending on whether you care about being able to return that system to its factory state at some point.
On a side note, the partition layouts of your Western Digital disks are very odd. Why are you using logical partitions on the 1TB disk? You've only got 4 total partitions, so they could all have been primary partitions. The 4TB disk has 5 total partitions, so at least two of them would need to have been logical partitions given that it's using the MBR layout, but even there it's odd that you have a primary partition AFTER those two. However, the much larger problem on that disk is that it's using the MBR layout despite having a 4TB capacity. That suggests that the disk is inside a USB enclosure that's employing a hack of sorts, and the impact of that hack is that the disk would be completely unreadable if you ever had to access it from outside that enclosure, e.g. if the enclosure electronics ever failed but the disk was still fine. See the "Update for USB enclosures" section of this KB article
. Unfortunately there isn't really a solution to that problem other than getting an enclosure that doesn't use that type of hack solution.
And just as a general note, I personally wouldn't really advise using separate partitions just for different backups. You could simply use folders on a single partition, and you'd end up with much more flexible use of your available disk capacity. Getting too "partition-happy" can cause you to end up with free space where you don't need it, and not enough capacity where you wish you had more.