OldCAFMember:
There is no Kyrie because it is sung as part of the litany
There was no litany of saints at that Mass in our Cathedral.
If I recall the rubrics correctly, the Litany is not sung if the font is not to be blessed. At the livestream I watched yesterday, the font was not blessed and the Litany was not sung. However, a small amount of water was blessed. Perhaps, small parishes did not bless fonts and maybe larger parishes or cathedrals did?
There is no Kyrie at the Mass, because this Mass is different from any other Mass. As you noticed, there is no traditional introduction (i.e. In the name of the Father…, The Lord be with You…, and the Penitential Act). This is because the Triduum, beginning with the Evening Mass of the Lord’s Supper is supposed to be one long liturgy, spread across three days. The Introductory Rites (including the Kyrie) are said on Holy Thursday and the traditional blessing does not come until at the conclusion of the Easter Vigil.
Normally on Holy Thursday there would not be a blessing at the end of the Mass making this fact all the more clearer, but most places did not celebrate a procession to the altar of repose and thus a blessing was required at the end of Mass on Holy Thursday.
If a parish celebrates the Vigil of Pentecost by combing it with Vespers, and then follows with several OT readings, as at the Easter Vigil, the Kyrie may be omitted. The Gloria is said after the last OT reading and its psalm and prayer, and Mass continues as normal.