I would suggest that you might want to pay a CPA to assist you in filling this document out (for the first time, anyway) as they generally have a very detailed understanding of the law and your obligations. But if you really prefer to do this yourself, you should read the IRS's instructions for form 1065 (which are quite long but very detailed and may be helpful if you're unsure what to put for a specific item). Be sure to scroll down or use the table of contents on the left, as the top part of that page is a listing of everything that has recently changed (which you likely don't need to care about, at least for your first time filing). It then goes on to give both general and specific instructions for the form, which is probably what you want to be reading.
Now, to your specific questions:
Is there any way to do this anonymously?
Heck no. Each partner will need to provide all of their personal information on a copy of Schedule K-1, which must be attached to Form 1065. Your real-world identities will be associated with this partnership, and with each other, like it or not.
Depending on how much you're willing to spend on this, you may be able to hire a lawyer, CPA, or tax preparer to act as a third-party intermediary. They would receive Schedule K-1 from each partner, compile the whole thing together, and then submit it to the IRS. As a result, you would be able to keep your identities secret from each other. If you're going to consult a CPA anyway, you may want to ask if this is a service they are willing to offer, or if they can give you a referral to someone who can do it.
[D]o I have to tell the government I am making a NSFW game?
Probably not. You have to list your "principal business activity" and "principal product or service," but the former is just a matter of picking a code out of this list, and the latter can (probably) just be "video games" or similar (assuming you call yourself a "software publisher"). They don't actually want to know what kind of game you're making. They just want a general category of business. In the event you get audited, they might ask you to demonstrate evidence for all of your business expenses, and in principle, they might also ask you to demonstrate evidence of revenue, but this is usually just a matter of showing them paystubs, invoices, etc. I would be rather surprised if they wanted to see the actual game itself, although I suppose anything is possible if (for whatever reason) they suspect you of committing fraud.
Regardless, it is very unlikely that the government will care that you're making an NSFW game. NSFW products are a big business, and perfectly legal (in most cases). It's much more likely that your bank will care.
Are they also going to file a form 1065?
No, the partnership files one for both of you. That means either you file it, or they file it, not both. But you will (probably) both need to both fill out schedule K-1 as discussed above.