In general, rules in D&D5 mean exactly what they say; no more, no less.
The relevant parts of the description are (my emphasis):
RING OF SPELL STORING
Ring, rare (requires attunement)
This ring stores spells cast into it, holding them until the
attuned wearer uses them. ...
Any creature can cast a spell of 1st through 5th level
into the ring by touching the ring as the spell is cast. ...
While wearing this ring, you can cast any spell stored
in it. The spell uses the slot level, spell save DC, spell
attack bonus, and spellcasting ability of the original
caster, but is otherwise treated as if you cast the spell. ...
Does the phrase 'any creature' bypass the attunement requirement?
You have to be an "attuned wearer" to use them and it is
petty clear the "original caster" and "you" can be different people. So, you do not need to be attuned to cast a spell into the ring; only out of it.
Does it allow the party's wizard to charge the fighter's ring of spell storing?