But the same paragraph instructs us to say these words when we walk on the road and when we sit in our house. We do not have a ritual to do either.
There are three opionions regarding Krias Shema:
The opinion (and some Rishonim stated it for the halacha, as Tosfot quoted below) following which even the first chapter's recitation is only a rabbinical mitsva.
Tosfot Sota 32a.
וליכא למימר דלא נקט אלא דאורייתא דהא בפרק מי שמתו (ברכות דף כא.) משמע דתפלה וקרית שמע דרבנן
It seems from the Gemara, chapter Mi Shemmeto (Brachot 21a), that Kriat Shema is a rabbinical commandment.
The gemara on Brachot 21a quoted by Tosfot asks your question against this opinion (Rav Yehuda amar Shmuel) for the words of the first chapter.
The recital of the Shema' is ordained only by the Rabbis, the saying of 'True and firm' is a Scriptural ordinance.
R`Joseph raised an objection to this, 'And when thou liest down, and when thou risest up'.
- Said Abaye to him: That was written with reference to words of Torah.
In this Gemara Berachot, there are two opinions regarding KS, Rabbi Yehuda in name of Shmuel, according to him KS is derabanan, and the Amora Rabbi El'azar (there are a couple of versions for this name), according to him it's deorayta.
The first two chapters are a scriptural mitzvah;
Only the first chapter is a scriptural mitzvah.
See the question and its answer in Gemara Berachot 13b regarding the second chapter (in this question we assume that the first chapter is a scriptural mitsva):
[Presumably] because it is written, 'upon thy heart and thou shalt speak of them? ' There too [in the second section] also it is written, 'upon your heart to speak.
of them'! These words have reference to words of Torah,
So for the opinion following which the recitation of the second chapter (but not the first) is a rabbinical mitsva, the verse "thou shall speak them" tells to speak divre tora, not particularly this chapter.
Regarding the halacha.
Rif, Rambam, Rosh in halachot Brachot, Rashba, Tur and SA ruled against Shmuel (contrarily to the Tosfot in Sota). And last poskim (Acharonim) followed this opinion.
Rishonim argued about the lenght of what is the stuff called KS in Gemara Berachot 21a..
There are several opinions.
Some Rishonim and Acharonim (Tshuvat Harashba 320, Rabbi Yehuda Hachasid in Tur 67 Bet Yosef, Magen Avraham and Baer Heytev there) is that the first verse only is a Mitsva deorayta. This opinion is based of a couple of statements in Masechet Berachot 13b, a testimony that Rabbi Yehuda Hanassi was saying this verse only, Tanayim opinion supported by Amorayim that this verse only needs Kavana, or needs full awareness.
The Rashba in Chiddushin in first Chapter regarding KS of bedtime and daf 21a , in name of Rabbi Shema'ya, Rabenu Yona, understand that the first chapter is deorayta. say that this is the first parasha only. This opinion is based on several rules regarding first chapter of Shema which are build on verses (in the second chapter of Brachot 16a and in Yoma). Some else say that the 3 first verses only are deorayta. The Sh'agat Arie stated as this opinion.
- The Pri Chaddash in SA OC siman 67 summarizes the diverses opinion in Gemara and poskim (he understands that Rambam's opinion (hilchot KS 1, 2) is that 2 parashiot are Deorayta, but the Sh'agat Arieh siman 2 argues strongly against this lecture on Rambam) state that the two first chapters are deorayta. Peri Chaddash follows this opinion.
- Aruch Hashulchan in siman 67 says that he rules, following his own understanding on Rambam that the 3 parashiot are deorayta.