The Catechism of the Catholic Church seems to allude to Rev 13:16 when it says:
The Church’s ultimate trial
675. Before Christ’s second coming the Church must pass through a final trial that will shake the faith of many believers. The persecution that accompanies her pilgrimage on earth will unveil the “mystery of iniquity” in the form of** a religious deception offering men an apparent solution to their problems at the price of apostasy from the truth.** The supreme religious deception is that of the Antichrist, a pseudo-messianism by which man glorifies himself in place of God and of his Messiah come in the flesh.
676. The Antichrist’s deception already begins to take shape in the world every time the claim is made to realize within history that messianic hope which can only be realized beyond history through the eschatological judgement. The Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism, especially the “intrinsically perverse” political form of a secular messianism.
677. The Church will enter the glory of the kingdom only through this final Passover, when she will follow her Lord in his death and Resurrection. The kingdom will be fulfilled, then, not by a historic triumph of the Church through a progressive ascendancy, but only by God’s victory over the final unleashing of evil, which will cause his Bride to come down from heaven. God’s triumph over the revolt of evil will take the form of the Last Judgement after the final cosmic upheaval of this passing world."
This is not official Church teaching but, concerning Rev 13:16, The International Bible Commentary: A Catholic and Ecumenical Commentary for the Twenty-First Century, ed. by William R. Farmer (The Liturgy Press, 1998), says, on page 1865:
Just as the Lamb puts his mark on his followers and thereby protects them (7:3; 9:4; 14:1), so too the beast marks those of his group, “all, both small and great, both rich and poor, both free and slave” (13:16). This mark, an important theme in the rest of the book (14:9, 11; 16:2; 19:20; 20:4) is “on the right hand or the forehead, . . . ‘the name of the beast’ or the number of its name” (13:16-17). The contrast with those who “had [the Lamb’s] name and his Father’s name written on their foreheads” (14:1) is obvious. It is therefore a religious mark, a sign and seal of belonging, of protection. The people submit to the beast, seeking his protection. the author uses the Greek word charagma that was used for the emperor’s seal (and not sphragis as in 7:3). This is the god who protects his people by enslaving them. To refuse to adore him is tantamount to excluding oneself from citizenship in the empire with all its attendant privileges (including economic ones). This is why the Christians’ situation is so awkward: either one enters into the game, with all the advantages it entails, or one becomes a stranger to that society and is excluded from it because one does not have the “party card” (the mark of the beast) (13:17). These are difficult times that call for faithful perseverance and standing firm in one’s witness (13:10 and 12:17)