Tallahassee Police Chief Michael DeLeo said the gunman acted alone and authorities were investigating possible motives.
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Beierle also argued against interracial relationships in the video, saying women who are in one have somehow betrayed "their blood".
Beierle, who was now living in Deltona, Florida, had served in the U.S. Army, police said.
Dr. Nancy Van Vessem was chief medical director for Florida's Capital Health Plan.
Beierle was arrested again in 2016 after allegedly grabbing and slapping the buttocks of a woman at an apartment complex's pool.
Police investigators work the scene of a shooting in Tallahassee, Fla.
The shooting Friday was in a small Tallahassee shopping center and multiple police cars and ambulances were on the scene. "No act of gun violence is acceptable", he wrote on Twitter.
According to the newspaper, Beierle was sympathetic toward Elliot Rodger, who killed six people and wounded 14 others in 2014 near the University of California, Santa Barbara. Beierle was a graduate of nearby Florida State University but he was living in a city in central Florida. Four of the wounded were in critical condition, DeLeo said.
'We just heard "pow, pow, pow, pow",' Mr Wesson said.
The two women who died were identified as a student and a faculty member from Florida State University.
Quick said Beierle was able to grab the gun back and then pistol-whipped him.
The police statement says, "Patrons fought the assailant to prevent him from harming themselves and others".
An FSU police report showed that Beierle told police he may have accidentally bumped into someone, but denied grabbing anyone.
Van Vessem was responsible for coordinating the third- and fourth-year clerkship rotations in internal medicine at the Tallahassee campus of Florida State, according to a profile on the university's website. Gillum said the two women he met "were in good spirits".
"They said that he came in and he had a black bag and he pulled it out and as [the gunman] went to go load it, all the yoga studio, the instructor and everybody started pounding on the windows and on the walls to let people know", Hutchinson said.
Beierle, a military veteran, also spoke angrily about the idea that women can press charges for his being "aggressive" in his pursuit of women, which he considered a typical "male characteristic".
Court records indicate prosecutors agreed to dismiss the battery charge after Beierle completed a six-month diversion agreement requiring him to stay out of trouble, not drink alcohol to excess and to follow a psychologist's recommendations.