After introducing the basic reasons for Chanukah, the *Kitzur Shulchan Aruch" writes:
ולכן י"א שמצוה להרבות קצת בסעודה בחנוכה, ועוד מפני שמלאכת המשכן נגמר בימים אלו, ויש לספר לב"ב ענין הניסים שנעשו לאבותנו בימים האלו, ומ"מ לא הוי סעודת מצוה אא"כ אומרים בסעודה שירות ותשבחות
Therefore, some say that there is a mitzva to increase somewhat in feasting, and also because the work of the mishkan was completed at this time. A person should tell over to his household the miracles that happened for our ancestors during these days. Nevertheless, it is not a seudas mitzva unless songs and praises are said by the meal.
To me, this language seems to indicate that the "songs and praises* only serve as the final condition. Meaning, given all of the previously stated reasons for why a Chanuka seudah should be a mitzva, the "songs and praises" are what close the deal. However, without all of those previous reasons, an ordinary meal with "songs and praises" would not qualify as a seudas mitzva.
This conclusion also appears to be explicit in the Mishneh Berurah (670:9), in his comment on the Remah's statement that if the meal is accompanied with songs and praises "אז הוי סעודת מצוה" - "then it is a seudas mitzva":
ואז הוי סעודת מצוה - ר"ל בצרוף זה. ... וכתב הרש"ל שכל שעושה כדי ליתן שבח למקום או לפרסם הנס או המצוה הכל סעודת מצוה
"And this is is a seudas mitva" - Meaning, in combination with this. ... And the Maharshal writes that any [seuda] made to give praise to God, or to publicize the miracle, or to publicize the mitzva, is a seudas mitzva.
The statement, "in combination with this", seems to clearly indicate that songs and praises by themselves cannot make a meal into a seudas mitzva. It is only when they are combined with other factors.
As for the underlying reasoning behind this, it seems that the basic definition of a seudas mitzva is a meal that one is specifically supposed to eat in fulfillment of a mitzva. This includes all Shabbos and Yom Tov meals, as well as meals associated with other mitzvos, such as a bris, a chasuna, or a siyum. In all of these cases, there is a mitzva, and often an outright obligation, to participate in the seudah. In other words, for a meal to be a true seudas mitzva, the seudah must qualify intrinsically as a mitzva (i.e. the mitzva is to eat).
By this definition, it is obvious that an ordinary meal with friends cannot become a seudas mitzva simply by adding "songs and praises". While singing songs and praises of God at an ordinary meal may be a very praiseworthy, they would not make the meal itself into a mitzva.
Chanuka, however, is a rather ambiguous case. Since there is apparently no actual obligation to make a seuda on Chanuka, all Chanuka meals would be considered seudas reshus. However, being that there are sources that indicate it is a mitzva to feast on Chanuka, when a Chanuka meal is combined with other factors (i.e. publicizing the miracle and singing praises to God), we do consider it a seudas mitzva.
I just looked up the Maharshal in Yam Shel Shlomo (Bava Kama 7:37). The Maharshal writes:
אלא נראה כל סעודה שאדם עושה שלא כדרך מריעות ושמחה, אלא כדי ליתן שבח למקום או לפרסם המצוה או לפרסם הנס קרוי סעודת מצוה, כגון פדיון הבן לפרסם המצוה
Rather, it seems that any seudah that a person makes, not in the manner of friendship and rejoicing, but for the purpose of giving praise to God, or to publicize [the performance of] a mitzva, or to publicize a miracle, is called a seudas mitzva, such as [the seuda by] a pidyon haben, which is to publicize a mitzva.
The Maharshal appears to be saying that everything depends on the purpose of the meal. This is not fully in agreement with the approach I presented above. I argued that there needs to be some intrinsic aspect of mitzva in the meal, but the Maharshal is saying that one can indeed simply create a seudas mitzva. However, even according to the Maharshal, the purpose of the meal must be the mitzva. One cannot simply convert an ordinary meal into a seudas mitzva by including praises of God.
Incidentally, the Maharshal also states, later in the same discussion, that there is a mitzva of seudah on Chanuka, and the seudos of Chanuka are seudos mitzva in their own right.