Fishbowl play, also occasionally called goldfish play, is an informal game term for playing without interacting with your opponent in any meaningful way. You're playing as if your opponent was a pet fish in a bowl. Playing solo and simply skipping all of your nonexistent opponent's actions and turns can be a useful way to see how reliable your Free Peoples deck sets up in early turns, or whether your hand is likely to clog with unplayable situational cards.
Alternately, the term can be used derisively to refer to a fishbowl deck, a deck strategy that involves simply ignoring your opponent and executing a game plan regardless of what they do. A Shadow deck that does all of its damage (be it wounds, burdens, or discard) in the Shadow and Maneuver phases offers the Free Peoples player little chance to prevent that damage, since such a deck probably doesn't care if its minions die in the Archery or Skirmish phases. These decks are often not very strong, but playing against them can be an NPE.
This term comes from the Magic: the Gathering community. In that game, testing to see how fast you can win without interacting with your opponent is somewhat more useful.