You mean "the homeowner WHO had stabbed the intruder" (the word "that" is only used in reference to inanimate objects, never people).

Regardless of grammar, it was never directly stated in the article that it was the homeowner who stabbed the intruder.  Read it again: 

"Male stabbed during East Anchorage home invasion"

"An East Anchorage home-invasion attempt left a male stabbed and critically injured early Friday, police said."

"When the homeowner confronted the male on his property, the stabbing took place."

Why all the passive voice constructions here?  It is as if the author purposely went WAY out of their way to avoid stating who performed the actual stabbing.  Why?  This is very poor reporting and writing as far as I'm concerned.