There are two assumptions I have here:

1. It has to do with the Windows 7 boot partition which has not been removed entirely.
There is a clear mentioning of it in your video, although I expect you will have tried to erase partitions and stuff a couple of times, just as shown in the video. So check with GParted from an independent source (I suggest Parted Magic: www.partedmagic.com) that this disk is actually clear and freshly formatted, and does not contain any hidden partitions.

2. It may have to do with the way the BIOS recognizes your hard drive.
Check what specifications your BIOS gives for the drive, and then compare them to a spec sheet as given by the manufacturer.
(Rather unlikely cause, but would explain the 'alignment' issue)

ps:

If possible, post a screenshot of the GParted window displaying the HDD partitions. There is a screenshot utility that comes with Parted Magic, and you may also access the internet via Parted Magic.

Fyi, it can be a problem installing Linux Mint 17.3 on "newer"(post-2009) SATA HDD that r 250GB or above in capacity bc of newer HDD technology = partitions not properly aligned with the disk. Something to do with 512 bytes data blocks in older IDE/PATA HDD(= came in 120GB or less sizes) n 4096 bytes data blocks in newer HDD. Eg the error message during installation = "... offset of 3584 bytes from minimum alignment ..."

If u get this error message during install of Linux Mint 17.3 on an external/USB HDD, u need to first use GParted to realign the modern hard disk, ie unmount the HDD, delete the whole old partition n create the 1st new partition meant for the "/" or root partition(eg 20GB in size), with 1 MiB(= the default value) at the "beginning of this space" n 0 MiB at the "end of this space", ensure "MiB" alignment box is checked(= do not select "cylinder"), set as Primary partition n format to fat32.
....... When creating the new 2nd partition meant for the home partition(eg 30GB in size), set 0 MiB for both the beginning n end of this space, Primary partition n format to fat32.
....... If u hv less than 4GB of RAM, u can also create a new 3rd partition for swap area(eg set as 2GB in size) for virtual memory/RAM on the hard disk, ... do as for the home partition above.
U can leave the remaining space as unallocated or free space. After the install, u can create a 4th new partition to store yr back-ups, movies, music, photos, files or install another Linux distro(= need to "sudo update-grub" to dual-boot).
Only then, can u proceed with the Install via the Live DVD or USB-stick. After clicking "Something else", click the 1st partition that u had created earlier with GParted, click "Change", click "ext 4 file system", click "/" for Mount point, n so on for the /home n swap partitions.
....... Ensure that the device for the bootloader is set to the external HDD, eg /dev/sdb or /dev/sdc. The cptr's internal HDD/SSD is usually identified as /dev/sda.
Seems, the Linux installer does not realign modern HDD when u create a "New Partition Table" for the "/"(root), /home n swap partitions during the install process.
I hv just successfully installed n booted LM 17.3 on a "modern" 250GB external/USB HDD which initially had the above error message about the 1st root partition not properly aligned with the HDD during install = could not proceed with the install. This was after many hours of reinstalling, trial n error.