One, he loves the attention.
Two, he did gain some legitimacy in the past with the Max Factor heir capture in Mexico.
https://www.theguardian.com/world/2003/jun/19/usa.mexico
Three, he is well known and has quite a following in the US. While he is a character who has been in prison, he also has no qualms about getting physical or tricking fugitives into being captured. In other words, he takes his job very seriously.
Four, any information he has on Gabby’s case has been turned over to the authorities, he is not being a hot dog but feels his ‘fame’ could get more leads since many in the US are interested in this case and apprehending this alledged murderer.
In regards to your comment on the ‘wild west’, if you’ve ever watched any of his shows, catching meth dealers and those types of criminals when they want to hide, is not easy. It sometimes takes someone with his credentials (former convict) to build trust. Plus many people know him and that he’s compassionate. He always lets them have a smoke, call their parents/family, and gives them good advice once they are in his custody.
He specifically said that likely the FBI and law enforcement will kill Laundrie instead of bringing him to justice in court, and that’s why he feels he needs to get involved. He doesn’t use lethal weapons in his captures.