Hi,
This sounds like it might be an import-and-split bug; I’ve been playing a little with that after reading a few other reports, which have included the ruler settings not applying properly to the first paragraph after the split. On the other hand, I’ve never seen it not automatically wrap, so I’ll have to investigate that further. (Needless to say, this is a bug, not a feature. 
) I gather that you’re seeing this for the entire document (not just the first paragraph), but is it only in the documents split off from the original? That is, if you go to the first document, the one you split the text out of, is the right indent set properly there? If it just imported wrong to start with, then split isn’t part of the issue, as that will just maintain the same formatting as the original document.
Also, just for clarification, when you say the right margin, do you mean the right indent? This would be the single upward pointing triangle on the right-hand side of the ruler (although its tool-tip does currently say “Right Margin”). Do you see it in the ruler at all, or is it entirely gone (even if you hide the inspector)?
Any additional details you can give would be great. How was the ruler set in the original Word document? What format did you import as (.doc, .rtf…)?
For correcting this, generally you could use the Documents>Convert to Default Formatting option to reset all the selected documents to the settings you define in Edit>Options in the Editor tab, but I’m leery of suggesting that as to reset the right indent it would likewise reset your left and first line indents and probably lose any bullets, which is probably highly undesirable if you’re working with a formatted outline. The best way to safely fix it is just to select all in the editor and then right click on the ruler (Ctrl-R first if it’s not visible) where you want the indent and choose “Set Right Margin” (again, this wording is off; it really means the right indent). You’ll need to do it for each document that’s exhibiting this behavior, so it might be easier to merge them all and do it and then redo the split (or re-import, explicitly set it in the imported document, and then split–since you applied the setting in Scrivener it should stick then after splitting).
If preserving bullets/indents isn’t an issue, then the conversion to defaults is definitely fastest. There’s a limitation on that in the current beta where the right indent can’t be set past about 5.5" in the options, but it will at least keep your text from scrolling off the screen, and it can be adjusted again once this bug is corrected. Set your defaults the way you like it in the Editor tab, then in the binder select the documents to convert and select the menu option. A dialogue will pop up giving you a list of options for the conversion: you’ll definitely want to check “preserve font styles” so you don’t lose italics and bold, etc., and you can choose whether you want to preserve any of the other options–the only one that matters for this is to not preserve tabs and indents.