How you would answer that question will depend on where you are in the program.
For example, if you are getting started entering W-2 information, and you do have a W-2 for that company, then answer 'yes'. That way the basic information about the company will already be there and it will not need to be entered.
Some state programs ask about the current employer. If this is your situation, then answer 'no' since there is a new company involved.
Either way, the answer is not likely to affect the tax return itself, so just answer to the best of your knowledge.
When you say "employed through a company" do you mean: now employed by the company that bought out his old company, or employed by the one that was bought out?
Seems to me that "company that bought out his old company" is a yes; and if a "the one that was bought out", the answer is no.
Yes, I believe your interpretation is correct.
If the question asked if he is still employed by 'old company that was bought out', then the answer would be 'no'. If the question asked if he is still employed by 'new company that bought out the old one', then the answer would be 'yes' if he does still work there.