First, I'm not an expert in this matter. I did a very fast (thus might miss details) reading of some of the pertinent background info.
First, you didn't state what kind of partnership this is, or what the partnership does. Having said that, it appears to me that if on Sch K-1 (F1065), if there are entries in lines 1-4 of the K-1, there is probably a US trade or business.
Generally, the other lines on Sch K-1 are for separately stated items that relate more to investment income/expenses that more relate to SCH NEC.
Generally, unless this is an investment type partnership, for which there is probably not any ordinary income or rental income, there is more than likely trade or business income. But here again, what does the partnership do? Does it conduct activities outside of the US?
What might complicate this a little bit more, is that US partnerships that have foreign partners, might/should have withheld taxes on the foreign partners. Does your Sch K-1 indicate that any taxes were withheld?
I suggest you do some more reading for the instructions for F1040NR
Pub 535 as it is referenced in the instructions
Instructions for Sch K-1 (1065)