However, the first paragraph of Shema, including this sentence, is a declaration of accepting G-d as King. From Quoting Berakhos 13a:
אמר רבי יהושע בן קרחה למה קדמה פרשת שמע לוהיה אם שמוע כדי שיקבל עליו עול מלכות שמים תחלה ואחר כך מקבל עליו עול מצות...
Rabbi Yehoshua ben Qorchah ("the bald one", ie the son of Rabbi Aqiva) said: Why does the paragraph of Shema come before that of VeHayah Im Shamoa? So that one accepts upon oneself ol Malkhus Shamayim -- the yoke of the Kingship of [the One in heaven] and after words accept upon oneself ol mitzvos -- the yoke of mitzvos....
So, the first paragraph is accepting G-d as my King. Not as a theory, but as a yoke I am harnessing myself to. To elaborate the "yoke" metaphor -- accepting G-d's rule as part of my means of being productive. (Followed by accepting his Mitzvos in the next paragraph of Shema.)
This is why we use the same verse as one of the 10 prooftexts in the berakhah of Malkhios in the Mussaf for Rosh haShanah, as it declares Hashem as our King.
Although on Rosh haShanah 32b, Rabbi Yehudah objects to the proposal, we rule otherwise. In an interesting essay, Rav Hutner (Pachad Yitzchaq, Rosh haShanah #11) says that Rabbi Yehudah is bothered about the difference in modality: Shema is accepting G-d as my King, in practice. Which may not fit Malkhios, which is a declaration of G-d as King in fact, whether I choose to be a loyal subject or not.
So this is what we mean when we say Hashem E-lokeinu -- Hashem is our G-d.
And when we say Hashem is One, it is in this context alone. I am ruling out dual loyalty -- He alone is my King.
This is why we're taught that when saying echad, there is a thought we're supposed to have for each letter relevant to Kingship. Shulchan Arukh Orakh Chaim 61:6:
צריך להאריך בחי"ת של אחד כדי שימליך הקב"ה בשמים ובארץ שלזה רומז החטוטרות שבאמצע הגג החי"ת ויאריך בדל"ת של אחד שיעור שיחשוב שהקב"ה יחיד בעולמו ומושל בד' רוחות העולם ולא יאריך יותר מכשיעור זה ויש נוהגים להטות הראש כפי המחשבה מעלה ומטה ולד' רוחות:
It is necessary to extend [the pronunciation of] the [letter] ches of [the word] echad (one) in order to make the Holy One, blessed be He, King in the Heavens and the Earth, in that this is hinted at in the humps in the middle of the roof of the chet. And one should extend the letter dalet of echad long enough to think that the Holy One, blessed be He, is unique in His world and rules in the four directions of the world, but he should not extend more than this amount. There are those who have the custom to turn the head in accordance with the thought: up, down, and to the four directions.
(Others associate the ches using gematria: Hashem is King over 7 heavens + 1 earth = 8, the numerical value of ches. As for extending the dalet, in his accent, the undotted version of dalet makes the /dh/ sound at the beginning of the word "this". As the Rambam describes it, "the sound a bee makes". There are Ashkenazim who try to make do with the Ashkenazi traditional sound, but err by ending up saying the non-word "Ech-ch-ch-a-a-a-a-deh". Can't extend by adding a vowel at the end.)
The Chafeitz Chaim went further, and warned about this thought of the Shulchan Arukh, "Don't be so busy accepting G-d as King of heavens and earth, across all four compass points of the world, that one forgets to accept Him as King over oneself!"
As a matter of theory, the unity of G-d means two things -- (1) that Hashem is Unique; and (2) that Hashem is indivisible. Remembering these two facts are two of the Six Constantly Applicable Mitzvos. So it's not terrible to have those in mind either. But as you see above, it's not the primary thrust of how our sages explain the word echad in the mitzvah of reciting this verse.