Generally speaking:
If you are a company employee, then any gifts you get are considered part of your taxable wages, even if it is a beneficial gift in a time of need, and should be included in your W-2 box 1 wages.
However,
the Share Fund appears to be set up as an independent tax-exempt charity. I think the goal was to make the gifts not be taxable income, because they come from the independent charity instead of from Staples Inc.
So my guess is that the viewpoint of the Share Fund is that it is charity assistance, which is not taxable to the recipient.
If the IRS ever gets around to looking at these kinds of arrangements, they might have a different point of view. But for now, as long as the money is not reported in your W-2 and you don't receive a 1099-MISC, the Share Fund is treating it as non-taxable charity assistance.