"theirs" is correct. Don't forget the form of the present continuous:
"Oracle are / is closing their doors and Microsoft are / is opening theirs."
A company can be referred to as a singular or plural entity.
"I am closing my doors and he is closing his"
"We are closing our doors and you are closing yours".
There is a little oddity in the language when it comes to "its"
"Brazil is selling its coffee beans but Argentina is not selling theirs".
Applying the same rule, it should really be "its" in both cases but "its" doesn't feel right and so we then use the word "theirs" to agree with "coffee beans" instead of "Argentina". I don't know the reason for this and I didn't realise it before. So thanks for the question.