Yes, as your system is slightly more capable than mine, you should be able to watch full HD video using VLC without problems even if VLC decodes H.264 in software.
I own a Lenovo Thinkpad R500 with P8400 @ 2.26 GHz and Radeon HD3450 graphics adapter running Windows 10. It's a system with slightly lower performance than your system and it plays H.264 encoded full HD video without recognizable frame loss. The CPU utilization is at 40% on average. I assume VLC is decoding video in software.
I watched the YouTube video you referenced using VLC 2.2.1. Its media information window provides the following statistics:
- Decoded : 2639 blocks
- Displayed: 2613 frames
- Lost : 1 frames
That being said, the full HD video playback using any browser as well as Microsoft's video app provide a stuttering and lagging video playback. Very unsatisfying.
If you are only asking how to enable hardware-supported video decoding on Ubuntu, I don't know the answer.