No, dialogue means any spoken words. There ar etypes of dialogue, and monologue might be a better term, but it's all teh same. First person POV is all dialogue, and the first person POV character is telling the reader the story orally, in dialogue, even if there are no quotation marks. The only way you can get consistent first person voice is to understand this.
The first person character is telling the reader the story, and whether you picture that character sitting across the table from you, or across the campfire from you, you're being told the story, and every word of it must be in the POV character's voice. You have to use his word choice, his cadence, his slang, his sense of humor, the works.
The dialogue he uses with quotation marks is what he says to other characters. The narrative without quotation marks are what he says to you.