I can’t guess what animal products were sent, please elaborate.

I think your tone and choice of words matters a lot, and tbh I would not have sent this complaint by email and instead gone to HR personally and ask them about it. In person you can convey your point with kindness in tone and depending on the culture of your workplace/country/area being vegan can rub some people the wrong way. A paid intern is not a high position within the company, so from their perspective it’s a new-ish employ emailing them an un thankful rejection email lecturing them on how to improve in their jobs by considering dietary restrictions. They may also not have had any say in the matter when it came to the gift, it could have been decided by someone above them for example. Modern HR would probably have considered dietary restrictions when it comes to gifts, but anyway.

In regards to what you do now.. go see them in person, say something like “Hey I’m sorry if there was a misunderstanding before, it’s great that the company is putting in effort to build a Christmas spirit but I and likely some others won’t be able to enjoy our gifts due to our dietary choices/restrictions”.

That’s it. Don’t bring up ethical arguments. You are an intern and the workplace is not your battleground to lecture your superiors on the evils of the meat industry. Apply some self preservation here and try and make friends with the people at work.