Microsoft has expensive lawyers on retainer, and would not challenge the takedown notice against youtube-dl.
Those lawyers protect Microsoft from liabilities.
Their users are, in this case, a liability.
Would Microsoft care about youtube-dl? Aside from their recent gesturing towards open source, I can't see a scenario in which they'd even say anything. Considering how often youtube-dl has to be updated and re-downloaded, they might even be happy to get that load off GitHub.
If they go after you for the same thing they themselves did aren't they just handing you the means to go after them?
They're not paying for your lawyers. It's that simple. Unless you have a deep war chest any competent lawyer would tell you not to pursue it.