The “Happy Father’s day” card was a surreptitious “I’m pregnant” announcement that first wasn’t understood by Guilliman because he is figuratively called the (gene)father of the Ultramarines and their various successor chapters. This was then clarified with the pregnancy test when drawn/photoshopped like that is a common meme among animé circles. In the fourth and fifth panels Guilliman has a moment of shocked understanding as to the meaning of the letter, and a psychic projection of the God-Emperor (essentially Guilliman’s Father) showing disapproval.

Now to clarify: The crowned Aeldari woman is Yvraine, emmisary and leader of the Ynnari (a mixed group of Aeldari who are attempting to bring back Ynnaed, the Eldar God of the Dead as a means of countering Slaanesh). The Ynnari had a whole thing near the end of Seventh Edition 40k in 2017 where among other things they allied with the Imperium against the 13th Black Crusade. Amongs that allyship, Yvraine with her mastery over death decided to bring Roboute Guilliman, the 13th Primarch, out of stasis with the help of a specially designed armor, the Mechanicus, and the Inquisition. Guilliman was downed and put into stasis on Ultramar some 9000 years prior after a fight with Fulgrim and had poison in his system. The armor and intervention of Yvraine let Guilliman finally be an active player in the setting where he did various things like become Lord Commander, have a meeting with the Emperor on the golden throne, start the Indomitus Crusade, and in various ways advance the setting a bit (the other big change is that Cadia has broken and a great rift in the warp has split the Galaxy in two). Not much has happened to the Ynnari since 2017, as the reception to the line / Army wasn’t enthusiastic and they even had a lore book cancelled. In the three editions since they just quietly made Ynnari not its own army anymore as they were just three new models and a headswap (or just palette swap) on some troops, and people didn’t like the “soup” aspect of just mixing in various knife ears together.

The internet being the internet, people saw that Guilliman and Yvraine were in the same room and concluded that they must be scoodilypoopin’ because opposite gendered people can’t ever just be friendly. In this fancomic, Guilliman is the “dad” of Yvraine’s implicitly announced unplanned child. The Emperor would likely be disapproving, as abhoring the alien is one of the core tenets of the Imperium. That said, in old canon there was indeed a half Eldar Ultramarine Librarian so hybrids are officially hypothetically possible, but that’s retconned out. I think Aeldari have a described triple helix DNA or something like that.