In nêhiyawêwin (Plains Cree) and other languages in the family, the "words" are as you say, more like "phrases".
The concept of "is" doesn't exist in the same way in nêhiyawêwin, it's often encoded in the verb itself, and the language (along with many Indigenous languages) have been called "verb-based" as opposed to "noun-based". Being "verb-based" (if we can describe it this way), the concept of "is" can often combined with what would be considered the "adjective" to come up with what you will see in the dictionary:
apisîsisiw - s/he is small
cimisisiw - s/he is short
iyinisiw - s/he is smart
(Note: that there aren't gendered pronouns in nêhiyawêwin, "s/he" really actually means "that one", however this is the definition you'll generally find in the dictionaries)
Further, verbs in the language will do what you expect, describe what the person is doing, or who they are interacting with:
atoskêw - s/he is working
mîcisow - s/he is eating
nipâw - s/he is sleeping
To further complicate matters, there is an intersection of "transitive" verbs (involving more than one person/object) and a "gender" of nouns that have been (for better or worse) classified as "animacy". Generally speaking, "living things" can be called "animate" and "non-living things" can be called "inanimate" (though there are many exceptions here), and the breakdown ends up creating four different verb classifications:
transitive verb + animate noun = VTA
transitive verb + inanimate noun = VTI
intransitive verb + animate noun = VAI
intransitive verb + inanimate noun = VII
Here's another view of the intersection of these concepts:
Here is an example of each:
wâpamêw [VTA] "s/he sees s.o."
wâpahtam [VTI] "s/he sees s.t."
wâpiw [VAI] "s/he sees; s/he has sight"
wâpan [VII] "it is dawn"
Now these forms are only so useful, because you aren't always just talking about the 3rd-person, so in order to talk about yourself, you need to inflect the verb to mean "me", for example:
"work"
nitatoskân "I work"
kitatoskân "you work"
atoskêw "that one works" (dictionary form)
atoskêwak "they all work"
nitatoskânân "we all work (but not you)"
kitatoskânâwâw "all of you work (but not me)"
kitatoskânaw "we all work"
atoskêyiwa "that (other) person works"
So. To answer your original question:
To me it feels like these "words" are really phrases or sentences. So I don't understand why they are included in a "dictionary". Can you please help me understand why?
They are really phrases, and the form that has been selected for the "lemma" (or "dictionary form") is generally the 3rd-person form, meaning the form you will generally see in the dictionary is usually "that one does XYZ", for consistency, and presumably also simplicity. In the case of transitive forms, you'll see the 3rd-person form again for VTI verbs, and the 3s -> 3' (third-person singular to fourth-person [or 'obviate']) form for VTAs. Further, verb inflections have have complex inflections and meaning, for instance:
ka-nakiskamohtahihcik (X actor -> 3p) "to be introduced to them by someone unspecified"
Coming from nakiskamohtahêw [VTA] "s/he introduces s.o."
, the above is possibly a poor choice for the lemma entry.
To also circle back to your earlier question:
Does Plains Cree not have infinitive verbs?
There is an infinitive inflection, again that could be specific to you or me (or anyone else) depending on the specific conjugation:
(once again using the "work" verb)
ta-atoskêyân "to work (me)"
ta-atoskêyan "to work (you)"
ta-atoskêt "to work (that one)"
ta-atoskêcik "to work (those ones)"
ta-atoskêyâhk "to work (all of us but not you)"
ta-atoskêyêk "to work (all of you, but not me)"
ta-atoskêyahk "to work (all of us)"
ta-atoskêyit "to work (that other person)"
An example of these used in-context might look like:
nimiywêyihtên ta-atoskêyân "I like to work"
[I like s.t.] [to work (me)]
One of these (infinitive forms) potentially could have been selected for use in the dictionary, but ultimately the form that is used currently (3rd-person singular independent conjugation) is the one that offers the most consistent experience for learners when attempting to utilize a verb within the conjugation paradigms, which exist for each verb type.
For that VAI verb above (atoskêw "s/he works"), here is an example of the possible inflections, not including "tenses":
For VAI verbs, there are only a couple dozen inflections (before tenses) but getting into the VTA paradigms, there are several hundred possible inflections, further underscoring the need to have a consistent entry for the dictionary.
You can view these conjugations on the itwêwina dictionary being developed by the University of Alberta.