The Gloria is required, but not because it is a Holy Day of Obligation. All Solemnities and Feasts are to include it, but not Memorials.
From the 2002 General Introduction to the Roman Missal (GIRM) which can be accessed from romanrite.com/girm.html :
“53. … It is sung or said on Sundays outside the Seasons of Advent and Lent, on solemnities and feasts, and at special celebrations of a more solemn character.”
The 2002 Roman Missal lists it specifically in the Mass for the Immaculate Conception of the Blessed Virgin Mary on 8 December. It has in Latin: “Dicitur Gloria in excelsis.” (Missale Romanum, Libreria Editrice Vaticana, 2002, ISBN: 8820972719, page 878.)