When the German Starbucks company (which actually is a Polish company Amrest Coffee) gives out a gift card an independent company in another company doesn't have to take it. They are just sharing a brand, but are different legal entities with independent ownership. (Franchise)
But even if it were the same company they could give out gift cards valid only in a single shop or something. Conditions have to be clear, though.
From the link I sent: “Starbucks Spain S.L. currently operates 90 stores in Spain and 11 stores in Portugal and plans to open 12 new stores and undertake integral renewal of 10 existing stores in Spain in 2016.”
The point is that “Starbucks Spain S.L.” is completely unrelated to “Starbucks Coffee Company” apart from licensing the brand from them since 2001 (I think it was a 50/50 joint venture until 2009 and later Starbucks had a non-controlling stake in 2013-2016).
But even if it were the same company they could give out gift cards valid only in a single shop or something. Conditions have to be clear, though.