Equipping from another minion you control
To equip with an equipment card currently possessed by one of your other minions, tap the acting minion (the minion who is attempting to get the equipment) and announce the equipment card he is getting. More than one equipment card can be taken from a minion in a single action. If the action is unsuccessful, the equipment remains where it is. (6.1.3)
No. Requirement only applies when you play the card (in the normal way should I add):
As you pointed out, nothing is specified when equipping from another minion (but it doesn't mean you'll be able to use it, depending on the cardtext).
Requirements for Playing Cards. Each library card has symbols on the attribute bar (the marble stripe on the left side) for the card type (except for master cards), the clan or Discipline (if any) required to play the card and the cost (if any) of playing that card. Some cards will have other requirements (such as capacity or title) stated in the card text. Only a minion who meets the requirements given on a minion card can play it, while only a Methuselah who controls a ready minion who meets the requirements of a master card can play it.
To be exhaustive, I'll add that "putting a card in play" in an exotic way (such as Alastor) isn't equipping, and therefore requirement doesn't apply (unless stated otherwise).