A yabam is not a non-spouse as we can see from the drashot below.
A yabam cannot annul the vows of the yebama
There is a berayta in Yevamot 29b:
שומרת יבם בין יבם אחד בין שני יבמין ר"א אומר יפר ר' יהושע אומר לאחד ולא לשנים דר' עקיבא אומר לא לאחד ולא לשנים
... Rabbi Akiva says, even when there is only one yabam, he cannot make hafarat nedarim for the yebama. The Gemara says that this Berayta is even after maamar.
The Rambam rules as Rabbi Akiva, Hilchot Nedarim 11:23:
שומרת יבם אפילו עשה בה יבמה מאמר ואפילו יבם אחד ליבמה אחת אינו מפר נדרי יבמתו עד שיבא עליה
A yabam cannot use the property of the yebama
See Gemara Yevamot 38a-39a. In 39a, the conclusion (opinion of Rava) of the Gemara is even Bet Shammai, and even after maamar (a kind of Kiddushin given by the yabam before ybum) she is Safek Jesus and cannot use her property.
The yabam can warn the yebama directly, the warning or a shomeret yabam is direct, not by the court. See Gemara 24ab
ורבי יונתן האי איש איש מאי עביד ליה
מיבעי ליה לרבות אשת חרש ואשת שוטה ואשת שעמום
The Gemara asks: And Rabbi Yonatan, who excludes both a betrothed woman and a widow awaiting her yavam from drinking the bitter water, what does he do with this term “any man”? What does it serve to include? The Gemara answers: Rabbi Yonatan requires it in order to include the wife of a deaf-mute and the wife of an imbecile, and the wife of mentally ill person [shiamum], whom the court warns on behalf of the husband.
You see that shomeret yabam isn't included in those whom the court warns on behalf of the husband.
The explanation of the Mishna.
The first interpretation of the gemara (24 a) and the conclusion is that is that our Mishna follows and makes the Drasha of Rabbi Yonatan (regarding the disagreement in berayta if Shomeret Yabam must drink).
(24a) And whose opinion is expressed in the mishna? It is the opinion of Rabbi Yonatan, as it is taught in a baraita with regard to the verse:....(24b) Rabbi Yonatan says: The phrase “while under your husband” excludes a widow awaiting her yavam from drinking the bitter water. Lest one would say that I will exclude a widow awaiting her yavam but I will not exclude a betrothed woman, the verse therefore states: “This is the law of jealousy, when a wife, while under her husband, goes astray, and is defiled” (Numbers 5:29). The term “while under her husband” excludes a betrothed woman from drinking the bitter water.
The Shomeret Yabam has some "stronger properties".
Rabbi Yoshia, who disagrees with Rabbi Yonatan, choices not to exclude her from the drinking because she is more wife than an Arusa, because she doesn't lack Chuppa (for this issue see Yevamot 29b)
Rabbi Yoshiya, holds that the bond with the widow awaiting her yavam is stronger, as she is not lacking entry into the wedding canopy, as her marriage to the yavam is completed through sexual intercourse alone. Rabbi Yoshiya therefore excludes only a betrothed woman from drinking the bitter water.
But she has "weaker properties", the kiddushin don't come from the Yabam himself, the Arusa is stronger, because the kiddushin are from the Arus himself. So, in the first Myut of the drasha he excluded Shomeret Yabam from drinkind, she is less similary to a common wife. From the first Myut (תחת אישך) he excluded Shomeret Yabam, from the second Myut (תחת אישה) he excluded Betrothed woman.
Further Gemara quotes a Drasha Rabbi Aba bar Chanina miDarom saying that there is no "drinking" for a woman who didn't sleep with her "husband" before sleeping with the "Boel". So why do we need the Drashot (תחת אישך, תחת אישה) of Rabbi Yonatan? (I don't explain the side of Rabbi Yoshia here) Gemara says that sometimes the Arus did make a intercourse of znut that is not Nisuyin. In this case we need the Drasha (תחת אישך) to exclude this case from Drinking.
And the Yavam, who makes an intercourse of Znut, despite a intercourse of znut is a valid. , has not all properties of Husband (following Shmuel opinion), so we need the second Drasha (תחת אישה) to exclude him from Drinking.
But Shmuel himself perhaps holds as Rabbi Yoshia (איש איש), and Shomeret Yabam will drink (more accurately Shomeret Yabam who had an intercourse of Znut with the Yabam) because of a Ribuy of Rabbi Yoshia, the ribbuy is a Chiddush that gives to the "shomeret Yabam" the status of wife.
In fine we can assume that the Drasha of of Rabbi Aba bar Chanina miDarom (מבלעדי אישך) is the main choice of the Gemara for a standard betrothed or Shomeret yabam, and the drasha of the Mishna, the drasha of Rabbi Yonatan is auxiliary for particular cases.
This is an explanation almost exhaustive of the Mishna.