What is meant by “we got a live one” in following context?

Barmer’s answer provides a solid and complete response to the OP’s specific question, I think. Nevertheless, it may be worth observing that “a live one” has several distinct slang meanings, as is clear from J. E. Lighter, Random House Historical Dictionary of American Slang (1997):

live one n. something or someone that is especially deserving of attention; Specif.:

1. Horse Racing. a fast horse. [Examples dating back to 1840 omitted.]

2.a. a person who is LIVE [that is, “exceptionally wide-awake or energetic; acute, ardent, full of life”]; (hence) one worthy of attention or favorable regard because of intelligence, skill, friendliness, or the like. [Examples dating back to 1896 omitted.]

b. something that is lively and interesting. [Example from 1909 omitted.]

3. Und[erworld]. a prospective victim of a swindle, esp. a wealthy, gullible person; one who can be easily taken in or exploited, esp. for money; SUCKER. [Examples dating back to 1908 omitted.]

In the OP’s video excerpt “live one” seems to mean simply “lively and interesting one,” but I have often seen “Looks like we’ve got a live one” used in scripts and novel dialogue to mean “looks like we’ve got sucker that we can take advantage of.” J. E. Lighter doesn’t include any examples of “live one” meaning “fast horse” more recent than 1907, bur it may still be used that way; in current U.S. baseball parlance, “a live one” refers to a good fastball in a pitcher’s repertoire of pitches (such a pitcher is sometimes said to have “a live arm”).