Both are short and sweet dramas about a modern day FL traveling to the past and falling in love with the historical ML. Eventually she returns to her time and meets a double of the ML at the end.

Both have emperor characters (ML vs. SML), the couple meeting due to time travel with the FL from modern day and the ML from the past, and are mini dramas in which the ML's double (or maybe the ML, it's ambiguous) appears in the present day at the ending.

Both are mini dramas with a main couple who meets and falls in love because of one of them time traveling to the other's time (but reversed in that EoG features a modern day character to the past, MYG is a historical character coming to present day). Both have the time traveler return to their own time, but meeting a doppelganger or possibly even the ML (it's ambiguous) in the present day,

The main couple is forced to marry because of a decree, and there is a love triangle with the SML who the FL only regards as a good friend.

Both are sweet and short romances with a similar vibe and pacing..
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Both are BL romances where one is the son of a gangster/mafia and the other works for the gangsters/mafia. Both couples must fight to stay together.

Both are historical dramas (Kingdom has fantasy elements, though) with gorgeous cinematography and a unique, rich autumn-like color palette. The ML in both is the only child of the prior king who dies in episode 1 and the queen who was of lower position which threatened/threatens his position. In both he has a childless stepmother who is scheming to have him killed.

Both have a modern day FL entering a game and accomplishing tasks to win. Both have a butler/guide character only the FL can see who helps her with her tasks and explains things in the game.

Both have the FL entering a game/drama world, and ending up becoming the queen of the royal ML Both are short, fun, and fast paced dramas.

In both, the FL enters a VR historical world in which she meets the royal ML
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Both are about a FL who travels to a historical era and must accomplish tasks to win the game and return home.

Both are about a FL who travels to a historical era and must accomplish tasks to win the game and return home, falling in love along the way.