I don't understand. You have described the way yourself, why do you need to ask?
You produce a label sheet with the specified requirements (there are several tutorials for that, one is here). This is a document, so you can save it as a document. Send it with the application/vnd.openxmlformats-officedocument.wordprocessingml.document MIME type (here the complete list) and you're good to go.
If you want to customize the DOCX server side, that can be done too (but in what language and with which tools? You need to specify that). There are several libraries to do that, or you can even do that by manipulating the XML inside the Zip container that's what a DOCX actually is.
Text only?
This is definitely not possibile with any binary format, so no DOCX or DOC.
But I very strongly suspect that it might be done by saving the file in RTF (Rich Text Format). Almost all of the MailMerge extensions are available (example) that are not available in HTML, and RTF files can be produced from plain text ASP pages.
So, I think that's your answer.
Pseudo-implementation
I did this by creating a Labels sheet and saving it in RTF format. Then, visually inspecting the file told me what needed to be done.
This is pseudo code, not ASP.
PRINTLN {\rtf1\ansi\deff3\adeflang1025
PRINTLN {\fonttbl{\f0\froman\fprq2\fcharset0 Times New Roman;}{\f1\froman\fprq2\fcharset2 Symbol;}{\f2\fswiss\fprq2\fcharset0 Arial;}{\f3\froman\fprq2\fcharset0 Liberation Serif{\*\falt Times New Roman};}{\f4\fswiss\fprq2\fcharset0 Liberation Sans{\*\falt Arial};}{\f5\fnil\fprq2\fcharset0 Microsoft YaHei;}{\f6\fswiss\fprq0\fcharset128 Lucida Sans;}{\f7\fnil\fprq2\fcharset0 Lucida Sans;}}
PRINTLN {\colortbl;\red0\green0\blue0;\red0\green0\blue255;\red0\green255\blue255;\red0\green255\blue0;\red255\green0\blue255;\red255\green0\blue0;\red255\green255\blue0;\red255\green255\blue255;\red0\green0\blue128;\red0\green128\blue128;\red0\green128\blue0;\red128\green0\blue128;\red128\green0\blue0;\red128\green128\blue0;\red128\green128\blue128;\red192\green192\blue192;}
PRINTLN {\stylesheet{\s0\snext0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1 Normal;}
PRINTLN {\s15\sbasedon0\snext16\dbch\af5\dbch\af7\afs28\sb240\sa120\keepn\loch\f4\fs28 Heading;}
PRINTLN {\s16\sbasedon0\snext16\sl276\slmult1\sb0\sa140 Text Body;}
PRINTLN {\s17\sbasedon16\snext17\dbch\af6\sl276\slmult1\sb0\sa140 List;}
PRINTLN {\s18\sbasedon0\snext18\dbch\af6\afs24\ai\sb120\sa120\noline\fs24\i Caption;}
PRINTLN {\s19\sbasedon0\snext19\dbch\af6\noline Index;}
PRINTLN {\s20\sbasedon0\snext20 Frame Contents;}
PRINTLN }{\*\userprops}\deftab709
PRINTLN \hyphauto1\viewscale100
PRINTLN {\*\pgdsctbl
PRINTLN {\pgdsc0\pgdscuse259\pgwsxn11906\pghsxn16838\marglsxn408\margtsxn859\pgdscnxt0 Default Style;}}\formshade\paperh16838\paperw11906\margl408\margr0\margt859\margb0\sectd\sbknone\sectunlocked1\pgwsxn11906\pghsxn16838\marglsxn408\margtsxn859\ftnbj\ftnstart1\ftnrstcont\ftnnar\aenddoc\aftnrstcont\aftnstart1\aftnnrlc
PRINTLN {\*\ftnsep\chftnsep}\pard\plain \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql\ltrpar\loch
Now the table begins. Margin is 408, width is 3600. By changing the values of the parameters \shptop, \shpbottom, \shpleft and \shpright, the cell is moved through the table.
PRINTLN {\shp{\*\shpinst\shpwr1\shptop859\shpbottom3019\shpleft408\shpright4008\shpz0{\sp{\sn shapeType}{\sv 202}}{\sp{\sn dxWrapDistLeft}{\sv 0}}{\sp{\sn dxWrapDistRight}{\sv 0}}{\sp{\sn dyWrapDistTop}{\sv 0}}{\sp{\sn dyWrapDistBottom}{\sv 0}}{\sp{\sn posrelv}{\sv 1}}{\sp{\sn posrelh}{\sv 1}}{\shptxt\s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql{
PRINTLN {\field{\*\fldinst MERGEFIELD Author }{\fldrslt <Author>}}}
PRINTLN \par \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql{
PRINTLN {\field{\*\fldinst MERGEFIELD Address }{\fldrslt <Address>}}}{
PRINTLN }
PRINTLN \par \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql\loch
PRINTLN \par \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql{
PRINTLN }
PRINTLN \par \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql\loch
PRINTLN \par \s0\hich\af3\dbch\af8\langfe2052\dbch\af7\afs24\alang1081\widctlpar\hyphpar0\ltrpar\cf0\loch\f3\fs24\lang1040\kerning1\ql{
PRINTLN }
PRINTLN \par \pard}}}
The end of the document is just
PRINTLN \par }
Tests in other formats
I have tested the other text formats that Word can turn out, and none of them can store a MailMerge label template. HTML appears to do it, but it doesn't actually work. XML might have done it, but it seems to be broken (the XML generated isn't read back properly. That might have been just me, though).
The other formats, as noted, are binary formats with a convoluted structure and can't be rendered easily using "two loops".
So, I feel confident that a "MIME document" with labels cannot be generated server side in ASP, because it cannot be generated in any way whatsoever using a text format (with the notable exception of RTF). There isn't any way the file can be formed.
So, how...?
Well, it turns out it is possible to "remote control" Windows Word, at least the old version, and do it from an ASP script using the Javascript OLE automation engine. The whole setup looks very much like what you described (ASP, simple tags, text formats), and I even wonder if any of these might be the basis for file you remember.
