It is explicitly forbidden by YouTube's TOS to play video back in any video player that is not controlled and/or approved by YouTube. Presumably this is so they can accurately track the video views, analytics, and enforce ads. That aside, even if they are your videos, you'd still be using YouTube's bandwidth to play them back without re-imbursing them. If you do a search on CDN bandwidth costs for streaming, you'll quickly see why they wouldn't be okay with that.
The relevant section from
YouTube's TOS:
"YouTube TOS, Section 4.C." wrote:
You agree not to access Content through any technology or means other than the video playback pages of the Service itself, the Embeddable Player, or other explicitly authorized means YouTube may designate.
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