In competition, you can only play a name if you know who the person is. No fair saying "Frank ... Johnson. That sounds like a real person! Let me just Google him real quick."
Dominoes is a family of boardgames played with rectangular "domino" tiles. A domino tile is divided into two squares, each displaying a number. Under most rules, a domino tile is placed on the table adjacent to another tile, and the adjacent ends must match in some way (usually by the number displayed on the touching ends). Randall's "name dominoes" shows a set of domino tiles with people's names instead of numbers, and adjacent tiles are matched by whether the closest name is the same (such as how Chris Evans' family name matches Evan Taylor Jones' given name). A large board is covered in rectangular "dominoes" (271 pieces), with each domino bearing the name of a "well-known" person or character (fictional). The dominoes are arranged as if a game of dominoes were being played, but instead of the game requiring the number of spots of adjacent dominoes to match up, this game requires adjacent names to match up. Because most people have two or more names, different matches are made at each end of a domino. Fun fact is that two of the people are "named after" the game: Fats Domino and Domino Harvey.
The match can be exact (e.g., "Kevin" on one domino adjacent to "Kevin" on another), homonymic (e.g., "Klein" adjacent to "Kline"), nickname-based (e.g., "James" adjacent to "Jimmy", which in turn is adjacent to "Jim"), or gender different versions of a name (e.g., "Olivia" adjacent to "Oliver"). Sometimes last names are matched up with first names (e.g., "Elizabeth Warren" adjacent to "Warren Beatty"), and in some cases only a single name is used (e.g., "Columbo", "Drake", "Garfield", "Prince"). Singular names are represented by a half-size square "domino" (or "monomino"), with a few exceptions: "Garnet" has a full-size tile (a complex reference explained below), and "Batman" and "Superman" have full-size tiles and are placed as though they were two-part names: the first square of "Superman" is matched with "Super", and the second square is matched with the second square of "Batman" (as though both characters had the last name "Man"). Some people have three or more names (e.g., "Frank Lloyd Wright") and have a 3-square domino tile (or "straight tromino", 50% longer than normal) which permits matching to a middle name (e.g. "Frank Lloyd Wright" is matched to "Lloyd Alexander" and "Harold Lloyd").
The names come from a wide variety of fields: scientists (e.g., Isaac Newton), historical figures (George Washington), musicians (Drake), politicians (John Kerry), actors (Kevin Costner), writers (Washington Irving), fashion designers (Oscar de la Renta), and so on. Most of the names are real people but a few are fictional characters, including some non-human characters like Garfield and Super Grover. In one case the nick name for a company is used: Ma Bell aka Bell System. Another "play on names" can be seen on 1529: Bracket.
One notable reference beyond just the use of a name is in the bottom left, there is the connection [ William Safire ][ Garnet ][ Ruby, Jack ]. The connection seems to be based on the fact that Sapphire, Garnet and Ruby are all gemstones, which does not match the implied rules of the game. This tile is a reference to the character Garnet in the cartoon Steven Universe, who is a "fusion" formed by two Gems: Ruby and Sapphire. Thus, the name "Garnet" is treated as though it was two names "Ruby" and "Sapphire", requiring a two-square tile despite having a one-word name. Randall has previously made references to this universe in 1608: Hoverboard. (See this and this image from that comic). Additionally, Ayn Rand, Paul Ryan and Rand Paul have been mentioned before, in the title text of 1277: Ayn Random. That idea may have been the prototype for this. Connecting Marilyn Manson with Marilyn Monroe and Charles Manson is likely a tongue-in-cheek reference, as the musician's stage name was literally chosen in the same way as this. In at least one case it is not entirely clear who is being referred to: "John Kelly" most likely refers to Gen. John F. Kelly, Donald Trump's chief of staff, but the name is extremely common and could equally refer to any number of people.
The title text spells out a rule that a player may only place a tile if they know who that person is. This is a variation of a rule in Scrabble, where a player loses a turn if their chosen word don't survive a dictionary challenge over the validity of the word. This rule implies that players are allowed to create new name dominoes tiles and that it is not a fixed set. In this case the player that is challenged has used the name Frank Johnson of which there are 12 exact matches on Wikipedia along with six with a middle name and more. (The player was likely trying to place a tile in the upper-left area of the board, in an attempt to connect the "Frank Vincent" and "Lyndon Johnson" dominoes. The move was subsequently made impossible when the "Francis Drake" domino was played.) In a google search as of the day the comic came out the first hit was Frank Johnson who is a retired American professional basketball player and coach. Randall has made several references to basketball in his comics.