As I understand it the Broncos didn't end their analytics department, they fired/parted ways with the head of it, while the department still exists. As far as I know, Broncos were one of only a handful of clubs that were using analytics in real time for play calling decisions. All clubs, including the Broncos still, using variety of analytics in scouting and other functions (many don't have internal departments, but use outside companies), but that's far different than being involved in game calling.
The timeout situation had nothing to do with firing the head of analytics, since all of us and the announcers knew timeouts needed to be called. If anything contributed to the issue, it was Fangio calling plays and being head coach and in charge of time outs.
This analytics things is much ado about nothing and has zero to do with the ownership situation.