Berachot 16a: How does ובלכתך בדרך exempt intercourse with a virgin?

On Berachot 16a, we read the following in the Mishna:

מתני' האומנין קורין בראש האילן ובראש הנדבך מה שאינן רשאין לעשות כן בתפלה חתן פטור מק"ש לילה הראשונה ועד מוצאי שבת אם לא עשה מעשה ומעשה בר"ג שנשא אשה וקרא לילה הראשונה אמרו לו תלמידיו למדתנו רבינו שחתן פטור מק"ש אמר להם איני שומע לכם לבטל הימני מלכות שמים אפי' שעה אחת:

Or, in English:

MISHNAH. WORKMEN MAY RECITE [THE SHEMA'] ON THE TOP OF A TREE OR THE TOP OF A SCAFFOLDING, A THING THEY ARE NOT ALLOWED TO DO IN THE CASE OF THE TEFILLAH. A BRIDEGROOM IS EXEMPT FROM THE RECITAL OF THE SHEMA' FROM THE FIRST NIGHT UNTIL THE END OF THE SABBATH, IF HE HAS NOT CONSUMMATED THE MARRIAGE.⁸  IT HAPPENED WITH R. GAMALIEL THAT WHEN HE MARRIED HE RECITED THE SHEMA ON THE FIRST NIGHT: SO HIS DISCIPLES SAID TO HIM: OUR MASTER, YOU HAVE TAUGHT US THAT A BRIDEGROOM IS EXEMPT FROM THE RECITAL OF THE SHEMA'. HE REPLIED TO THEM: I WILL NOT LISTEN TO YOU TO REMOVE FROM MYSELF THE KINGSHIP OF HEAVEN EVEN FOR A MOMENT.

In the gemara, this is clarified, via a brayta, to refer specifically to a betula, but an almana (or gerusha; meaning a non-betula), no.

חתן פטור מק"ש:

תנו רבנן בשבתך בביתך פרט לעוסק במצוה ובלכתך בדרך פרט לחתן מכאן אמרו הכונס את הבתולה פטור ואת האלמנה חייב

A BRIDEGROOM IS EXEMPT FROM RECITING THE SHEMA'.²⁴  Our Rabbis taught: 'When thou sittest in thy house': this excludes one engaged in the performance of a religious duty. 'And when thou walkest by the way': this excludes a bridegroom. Hence they deduced the rule that one who marries a virgin is exempt, while one who marries a widow is not exempt.

In the Tosefta, meanwhile, chatanim are exempt from a different part of the pasuk; that is, the two prooftexts of the above brayta are reversed!

א,ה  החתנים וכל העוסקין במצות פטורין מק"ש ומן התפלה ומן התפילין שנאמר (דברים ו) בשבתך בביתך פרט לחתנים ובלכתך בדרך פרט לעסוקין במצות.

In the Yerushalmi, the derasha is the same as in our gemara:

בשבתך בביתך פרט לעוסקים במצות ובלכתך בדרך פרט לחתן.

In the Yerushalmi (Berachot 8b), one Amora is prepared to interpret the Mishna as referring to specifically an almana. Though in the end, it seems that it is interpreted as referring specifically to a betula:

דף יח, ב פרק ב הלכה ו גמרא  ר' אלעזר בן אנטיגנוס בשם ר' אליעזר בי ר' ינאי זאת אומרת שמותר לבעול בעילה בתחילה בשבת.  א"ר חגיי קומי ר' יוסה תיפתר באלמנה שאינה עושה חבורה.  א"ל והא תנינן ארבעה לילות אית לך למימר ארבעה לילות באלמנה.

Soncino (at least on daf 11, where thus sugya also occurs) reverses the text of the brayta to accord with the Tosefta, noting:

This is the reading of MS.M., and this is the version found in Tosaf. Suk. 25a a.v. [H] and elsewhere. Cur. edd. reverse the positions of 'bridegroom' and 'one who is occupied, etc.'

Back to our gemara, after the citation of the brayta, Rav Pappa (or in Succah 25a, Rav Huna) then gives the derivation, in the sense of ובלכתך בדרך meaning a devar reshus rather than a devar mitzvah, and bringing in the issue of agitation, which would prevent one from focusing on Shema while engaged in this mitzvah. All of this is somewhat strange since the brayta explicitly derives osek bemitzvah and chatan from different parts of the pasuk. But maybe כי דרך is drawing a parallel between the two. Thus:

מאי משמע אמר רב פפא כי דרך מה דרך רשות אף הכא נמי רשות מי לא עסקינן דקאזיל לדבר מצוה ואפילו הכי אמר רחמנא ליקרי אם כן לימא קרא בלכת מאי בלכתך שמע מינה בלכת דידך הוא דמחייבת הא דמצוה פטירת אי הכי מאי איריא הכונס את הבתולה אפי' כונס את האלמנה נמי הכא טריד והכא לא טריד אי משום טרדא אפילו טבעה ספינתו בים נמי אלמה אמר רבי אבא בר זבדא אמר רב אבל חייב בכל מצות האמורות בתורה חוץ מן התפילין שהרי נאמר בהן פאר שנאמר(יחזקאל כד, יז) פארך חבוש עליך וגו' אמרי התם טרדא דרשות הכא טרדא דמצוה:

How is this derived? — R. Papa said: [The sitting in the house] is compared to the way: just as the way is optional, so here it must be optional. But are we not dealing [in the words 'walkest by the way'] with one who goes to perform a religious duty, and even so the All-Merciful said that he should recite? — If that were so, the text should say, 'in going'. What is meant by 'in thy going'? This teaches that it is in thy going that thou art under obligation, and in the going for a religious duty thou art exempt. If that is the case, why does it say, 'One who marries a virgin'? The same would apply to one who marries a widow! — In the former case he is agitated, in the latter case he is not agitated. If his agitation is the ground, then even if his ship has sunk in the sea he should also be exempt? [And if this is so], why then has R. Abba b. Zabda said in the name of Rab: A mourner is under obligation to perform all the precepts laid down in the Torah except that of tefillin, because they are called 'headtire', as it says, 'Thy headtire bound upon thy head' etc.? — The reply is: There the agitation is over an optional matter, here it is over a religious duty.

The translation from Soncino provides the analogy, that כי דרך means "[The sitting in the house] is compared to the way". Perhaps. It still seems like this is a conflation of the two parts of the pasuk. And so, one who marries should be encompassed under the same category as anyone else who is tarud bidvar mitzvah, so why have a special limud?

Also, Rav Pappa seems to be dealing with the brayta as it appears in the Tosefta, rather than it appears in our gemara. After all, he takes  עוסק במצוה  as reshus, to the exclusion of עוסק במצוה. But our brayta understood the prooftext of ובלכתך בדרך to refer to the chatan, and בשבתך בביתך as referring to the exclusion of עוסק במצוה! This indicates to me that the reversal suggested by Soncino has even further basis. We would need to similarly emend the Yerushalmi -- or consult manuscripts, perhaps.

If I were pressed to explain how עוסק במצוה is to yield פרט לחתן, and particularly הכונס את הבתולה, I would have a ready answer in Mishlei 30:19:

יט  דֶּרֶךְ הַנֶּשֶׁר, בַּשָּׁמַיִם--    דֶּרֶךְ נָחָשׁ, עֲלֵי-צוּר; דֶּרֶךְ-אֳנִיָּה בְלֶב-יָם--    וְדֶרֶךְ גֶּבֶר בְּעַלְמָה.	19 The way of an eagle in the air; the way of a serpent upon a rock; {N} the way of a ship in the midst of the sea; and the way of a man with a young woman.
כ  כֵּן, דֶּרֶךְ אִשָּׁה--    מְנָאָפֶת: אָכְלָה, וּמָחֲתָה פִיהָ;    וְאָמְרָה, לֹא-פָעַלְתִּי אָוֶן.	20 So is the way of an adulterous woman; {N} she eateth, and wipeth her mouth, and saith: 'I have done no wickedness.' {P}

We see explicitly that the way of intercourse a man has with a young, non-virgin, woman, is called דרך. (It does not specify בתולה and consider the next pasuk, that there is no trace of the act after it is finished; just as the say of a ship amidst the sea, which leaves no permanent trace.)

Thus, ובלכתך בדרך refers to intercourse with a non-virgin. But with a virgin, it is not called derech, and so we have our פרט.

See this shiur by Rav Herschel Schachter, where he mentions how Ramban and Ritva distinguished between asmachta and asmachta bealma. The former is an asmachta chashuva and represents a real implication of the pasuk, with Hashem alluding to the future din derabbanan, yet not making it binding as a deoraysa; and the former, an asmachta bealma, is a mere mnemonic device.

In terms of my derivation above, this would be a real derasha. Yet, it is also a literal asmachta be'alma! :)