Евгений Ромашов

const players = {
    player1: {
      attack: 5,
      defense: 3,
      speed: 5,
      control: 5,
      strike: 5,
      stateOnSat: false
    },
    player2: {
      attack: 3,
      defense: 5,
      speed: 4,
      control: 4,
      strike: 5,
      stateOnSat: false
    }
  }

  const btnPlus = document.querySelectorAll('.btn-plus')

  btnPlus[0].onclick = () => {
    players.player1.stateOnSat = true
    alert(players.player1.stateOnSat) // true
  }

  // Или 
  btnPlus[1].addEventListener('click', () => {
    players.player2.stateOnSat = true
  })

<button class="fas fa-plus-square btn btn-plus" onclick="players.player2.stateOnSat = true">Plus</button>