Does "Going Infinite" necessarily end the game?
The comprehensive rules on taking shortcuts in Magic, as per your request. (Sorry, long...)

If you refuse to take a shortcut out of an infinite loop when you have the opportunity, you are committing deliberate timewasting as Andrey's answer suggests; a definite no-no in a tournament, and hopefully in a friendly group as well!


  
  Taking Shortcuts
  
  
  715.1. When playing a game, players typically make use of mutually
  understood shortcuts rather than explicitly identifying each game
  choice (either taking an action or passing priority) a player makes.
  
  715.1a The rules for taking shortcuts are largely unformalized. As
  long as each player in the game understands the intent of each other
  player, any shortcut system they use is acceptable.
  
  715.1b Occasionally the game gets into a state in which a set of
  actions could be repeated indefinitely (thus creating a "loop"). In
  that case, the shortcut rules can be used to determine how many times
  those actions are repeated without having to actually perform them,
  and how the loop is broken.
  
  715.2. Taking a shortcut follows the following procedure.
  
  715.2a At any point in the game, the player with priority may suggest
  a shortcut by describing a sequence of game choices, for all players,
  that may be legally taken based on the current game state and the
  predictable results of the sequence of choices. This sequence may be a
  non-repetitive series of choices, a loop that repeats a specified
  number of times, multiple loops, or nested loops, and may even cross
  multiple turns. It can't include conditional actions, where the
  outcome of a game event determines the next action a player takes. The
  ending point of this sequence must be a place where a player has
  priority, though it need not be the player proposing the shortcut.
  Example: A player controls a creature enchanted by Presence of Gond,
  which grants the creature the ability "{T}: Put a 1/1 green Elf
  Warrior creature token onto the battlefield," and another player
  controls Intruder Alarm, which reads, in part, "Whenever a creature
  enters the battlefield, untap all creatures." When the player has
  priority, he may suggest "I'll create a million tokens," indicating
  the sequence of activating the creature's ability, all players passing
  priority, letting the creature's ability resolve and put a token onto
  the battlefield (which causes Intruder Alarm's ability to trigger),
  Intruder Alarm's controller putting that triggered ability on the
  stack, all players passing priority, Intruder Alarm's triggered
  ability resolving, all players passing priority until the player
  proposing the shortcut has priority, and repeating that sequence
  999,999 more times, ending just after the last token-creating ability
  resolves.
  
  715.2b Each other player, in turn order starting after the player who
  suggested the shortcut, may either accept the proposed sequence, or
  shorten it by naming a place where he or she will make a game choice
  that's different than what's been proposed. (The player doesn't need
  to specify at this time what the new choice will be.) This place
  becomes the new ending point of the proposed sequence. Example: The
  active player draws a card during her draw step, then says, "Go." The
  nonactive player is holding Into the Fray (an instant that says
  "Target creature attacks this turn if able") and says, "I'd like to
  cast a spell during your beginning of combat step." The current
  proposed shortcut is that all players pass priority at all
  opportunities during the turn until the nonactive player has priority
  during the beginning of combat step.
  
  715.2c Once the last player has either accepted or shortened the
  shortcut proposal, the shortcut is taken. The game advances to the
  last proposed ending point, with all game choices contained in the
  shortcut proposal having been taken. If the shortcut was shortened
  from the original proposal, the player who now has priority must make
  a different game choice than what was originally proposed for that
  player.
  
  715.3. Sometimes a loop can be fragmented, meaning that each player
  involved in the loop performs an independent action that results in
  the same game state being reached multiple times. If that happens, the
  active player (or, if the active player is not involved in the loop,
  the first player in turn order who is involved) must then make a
  different game choice so the loop does not continue. Example: In a
  two-player game, the active player controls a creature with the
  ability "{0}: [This creature] gains flying," the nonactive player
  controls a permanent with the ability "{0}: Target creature loses
  flying," and nothing in the game cares how many times an ability has
  been activated. Say the active player activates his creature's
  ability, it resolves, then the nonactive player activates her
  permanent's ability targeting that creature, and it resolves. This
  returns the game to a game state it was at before. The active player
  must make a different game choice (in other words, anything other than
  activating that creature's ability again). The creature doesn't have
  flying. Note that the nonactive player could have prevented the
  fragmented loop simply by not activating her permanent's ability, in
  which case the creature would have had flying. The nonactive player
  always has the final choice and is therefore able to determine whether
  the creature has flying.
  
  715.4. If a loop contains only mandatory actions, the game is a draw.
  (See rules 104.4b and 104.4f.)
  
  715.5. No player can be forced to perform an action that would end a
  loop other than actions called for by objects involved in the loop.
  Example: A player controls Seal of Cleansing, an enchantment that
  reads, "Sacrifice Seal of Cleansing: Destroy target artifact or
  enchantment." A mandatory loop that involves an artifact begins. The
  player is not forced to sacrifice Seal of Cleansing to destroy the
  artifact and end the loop.
  
  715.6. If a loop contains an effect that says "[A] unless [B]," where
  [A] and [B] are each actions, no player can be forced to perform [B]
  to break the loop. If no player chooses to perform [B], the loop will
  continue as though [A] were mandatory.