The company saves money on various overhead expenses during that time such as running the lights, air-conditioning/heating, staffing the cafeteria, not needing as many security guards on duty, less pc's powered on, first aid supplies being used up, etc.
Even if they didn't shut down, a significant portion of their staff will probably be on vacation anyway since people travel for the holidays, schools are closed and they may not have childcare, etc. With such a reduced staff available to work, the amount of work that can be gotten done rapidly decreases. Key decision makers aren't available to resolve design decisions. Collaborators who know how a system is designed aren't there to answer questions. Subcontractor's office is closed. etc. Plus those at work may have reduced morale and productivity. Many people, intentionally or not, may work at a slower pace or spend more time chit-chatting or doing stuff unrelated to work, or goofing off in some way.
Additionally, having a complete shutdown allows the company to do scheduled maintenance on the actual facility that would take longer than a weekend, without the risks of employees being in the way/injured/inconvenienced/etc. Or they may want to have auditors do inventory or other tasks that may be easier an empty office.
And then there's also the type of person who is a bit of a workaholic and will not take any vacation or other downtime ever unless it is forced upon them, such as in a shutdown situation. So a shutdown may help prevent burnout and keep employees more balanced as a whole (even though, financially, it may work to the disadvantage to those who are forced to take an unpaid day off or more).