Loyalty is not the same thing that loyalty counters. Non-planeswalker creatures don't have loyalty, but the can have loyalty counters. So, if a (+) loyalty ability is played, then we add that many loyalty counters to the creature. If a (-) loyalty ability is played, then we remove that many loyalty counters from the creature.
Remember that we can only play activated abilities if we can pay the cost, and loyalty abilities are activated abilities, so we can't play a (-) ability if we don't have enough counters.
306.5. Loyalty is a characteristic only planeswalkers have.
306.5a The loyalty of a planeswalker not on the battlefield is equal to the number printed in its lower right corner.
306.5b A planeswalker is treated as if its text box included, “This permanent enters the battlefield with a number of loyalty counters on
it equal to its printed loyalty number.” This ability creates a
replacement effect (see rule 614.1c).
306.5c The loyalty of a planeswalker on the battlefield is equal to the number of loyalty counters on it.
306.5d Each planeswalker has a number of loyalty abilities, which are activated abilities with loyalty symbols in their costs. Loyalty
abilities follow special rules: A player may activate a loyalty
ability of a permanent he or she controls any time he or she has
priority and the stack is empty during a main phase of his or her
turn, but only if none of that permanent’s loyalty abilities have been
activated that turn. See rule 606, “Loyalty Abilities.”
As we can see, the loyalty of a planeswalker on the battlefield is linked to the number of loyalty counters on it. But nothing stops a non-planeswalker permanent from having loyalty counters or loyalty abilities.
However, as rule 306.5d indicates, all permanents with loyalty abilities, not just planeswalkers, may only use their loyalty abilities at sorcery speed and once per turn.