What kind of character does a person who makes loud exclamations have?

The adjective boisterous might well answer. OED offers “Abounding in rough but good-natured activity bordering upon excess, such as proceeds from unchecked exuberance of spirits”; Merriam-Webster makes it “very noisy and active in a lively way.”


Rambunctious is a relatively new North American expression that parallels boisterous:

adjective

  1. difficult to control or handle; wildly boisterous:

  2. turbulently active and noisy:


Another possibility is ebullient:

ebullience - Vocabulary.com

Bubbly, loud, and enthusiastic: ebullience means "the quality of being cheerful and full of energy."

synonyms:

exuberant, buoyant, cheerful, joyful, cheery, merry, sunny, breezy, jaunty, light-hearted, in high spirits, high-spirited, exhilarated, elated, euphoric, jubilant, animated, sparkling, effervescent, vivacious, enthusiastic, irrepressible

[Google Dictionary as was]


I would describe the way the woman in the video expresses herself as emphatic:

  • speaking or acting in a forceful way.

  • forceful and definite in expression or action.

(from W-W)


You can say the woman is

  • "rumbustious" ("Uncontrollably exuberant" - TFD)
  • "rumbustiously outspoken"
  • "rumbustiously spontaneous"

Brian Donovan's answer, "boisterous", is a single word and fits better what you are looking for, though.