You seem to have two related but distinct problems:
Your team has been set unrealistic goals (or rather, the goals are creeping into unrealistic territory). There isn't enough time to do the work required. This is a common problem, you have to reduce your targets or increase your resources or somehow find ways to be more efficient.
You have a strong opinion about how to reduce your targets, that your boss doesn't share. So, you either have to change his mind or suck it up. It seems obvious to you that this work on employees' home equipment isn't critical to the business, but if your boss and the owner of the company both want it done, then generally speaking their opinion as to what the company should be doing takes priority over yours, on account of the definition of "boss".
Personally, it seems to me that tech support on home equipment used for work is quite important to the company's mission, whereas "fix my son's XBox" is not mission-critical but might be indirectly beneficial to the company as a bonus for staff morale. If your boss understands the extent of the work, and the cost to the department in doing it, and still wants it prioritised to the detriment of other concerns, then do it.
If you're doing tech support for 1000 people then presumably you have quite a large team already, and a huge number of ongoing tasks. I'll wager that you already know how to tell people that, for a given request, they aren't going to get everything they want at the time they want it, and that managing expectations is routine for you. So do some of that: the only question is whether to do it for personal support requests or other requests, and that comes down to what kinds of task your organisation wants you to prioritise over others.
The only "legalistic" route I can think of to take, is to ask the accountant how you should be reporting the fair market value of the benefit in kind that employees are receiving (free tech support for their personal equipment) for tax purposes. Depending on your relationship with the accountant and your boss, this move might be all fun and games, or it might be a high-risk powerplay that results in you being fired for obstructiveness or whistle-blowing. Judge the situation on the ground.
The company can't force you to do personal favours for other employees, but since tech support is your job description it's hardly a stretch for them to ask you to do tech support, up to and including contracting you out as tech support for other companies, or (as in this case) doing tech support for others as a "favour" by the company. The difficult part is that they're stretching you and your team to the limit of how much free overtime you'll do. This is always a problem with salaried workers and grasping bosses: the fact that you think the work is pointless increases your frustration with the situation, but it doesn't fundamentally change the scenario you're in. Which is standard employer-employee conflict over the extent of unpaid overtime.