I have been unable to duplicate the EaseUS problem on a Legacy Windows 8.1 install, although the System partition not having a label looks suspicious. It should show as System Reserved, so the fact it does not, might be some indication. Have you done anything to alter that partition?
How are you getting to the page in the attachment? Are you starting in Windows, or booting to some recovery/install media or F key?
Edit: Is the attachment from your actual 8.1 system or from another install of Windows 8?
AeonWorld's post has confused the issue....I will have to reconsider the situation when the OP responds......
[DEL]I suppose I am a little concerned about the possibility HP has some special setup that causes the partition to appear that way. [/DEL] So I have changed the post until we confirm your status. You can check the attachment below, which is for a UEFI install, and see if you show OEM for that partition as it does.
Would you please go into the Admin command Prompt again and use Diskpart to select the partition and then do a detail partition command to make sure of the ID currently on it.
sel dis 0
sel par 1
An attach the results. Hopefully is shows as Type ID of 07.. If it does, then I will repost the procedure so you can try it.