Well, that was mostly the cynic in me writing, but on the other hand, isn't a threat made against a single individual typically handled by the police? Why would FBI feel the need to get involved? Or is this on of the "because it happened on the Internet it's different" kind of situations?
Government agencies overstepping their boundaries and getting involved in things that aren't their business is certainly a reason for concern.
Why what police force get involved when...
This is a basic, 50,000 foot view; it's not intended to cover all the details, and corrections gratefully accepted, but I believe this covers the gist of it...
It's pretty clear that the threats, particularly against the appearance of Anita Sarkeesian at Utah State University were, at a minimum, interstate.
When the threats cross a state line, the move from local police jurisdiction to federal police (FBI) jurisdiction, since police forces may only operate within their own jurisdictions. If the crime spans larger jurisdictions, such as adjacent cities within a county, or adjacent counties within a state, then it may be handled by an inter-agency task force. If it gets bigger than that, then the next larger jurisdiction encapsulating the jurisdictions involved takes ownership. The jurisdictions and agencies, are as follows:
Within a city: The city police force
Within a county: The county sheriff
Within a state: The CBI (California Bureau of Investigation - agency name varies by state)
Interstate: The FBI
Within these classifications, inferior jurisdictions are often acted to cooperate/participate in the investigatory legwork, arrest operations, searches, evidence gathering, forensic work (autopsy, crime scene investigation, and so on).
When a crime occurs on a federal lands or reservations, the FBI always has jurisdiction. For "indian reservations", investigator power lies in both the FBI and in the tribal police force (depending on the nature of the crime).
When a crime occurs on a military base, the investigatory power lies within the branch of the military; for most crimes, this is the MPs or Military Police. For more serious crime, or crimes involving military personnel not on base, or non-military and military personnel both, it goes by branch of service:
Navy, Marine, Coast Guard: NCIS - Naval Criminal Investigative Service
Army: USACIDC or CID - Criminal Investigation Division of the Army Provost's office
Air Force: AFOSI or OSI - Office of Special Investigations
Generally, anything involving a civilian, or occurring off base, ands up being a joint investigation with local authorities, which can include authorities in other countries (e.g. naval bases in Japan, air force bases in Germany, etc.).
For terrorist threats, USDHS - DHS - the Department of Homeland Security - gets involved. They are probably already involved in the Utah State University threat. At that pint, they can call on the capabilities and services of agencies such as the DOJ (Federal Marshals office), the NSA (which is allowed to operate domestically), the CIA (which is allowed to operate extranationally), the DIA (which is allowed to operate with regard to foreign military), and so on.
All in all, the more something escalates in terms of geographic reach, or in terms of threat level, the higher up the food chain you go, further and further into territories where you do not want to be. At some point in the escalation process, you get to the stratospheric regions where people simply "disappear" (otherwise known as "extraordinary rendition").
Does that answer your question?