Thank you Juanito for help. Now https links works and Tinycore has up to date software.
I would like to also add some comments.
1) mplayer-cli dependencies have 100 MB. Mplayer with internal ffmpeg would have only 16 MB or even less using upx.
2) I found that "due to conflicting MPlayer and OpenSSL licenses the
resulting binary may be non-distributable"
3) mplayer.tcz.info shows version 1.1.1 instead 1.3.0
4) mplayer volume control don't work in my computer. PCM value is changing but sound is still at the same level.
5) m3u8 protocol streams signal in packets, and it creates freezes. As I read it was ffmpeg fault not mplayer, but I think in latest mplayer snapshot, it was fixed (with internal ffmpeg).
http://lists.mplayerhq.hu/pipermail/mplayer-users/2013-September/086606.html6) What is also interesting some servers may be not compatible with gnutls. This means that mplayer may not work with all https links.