Using the times of injection and retrofire in this diagram:
and the orbit information from NASA, I get that Yuri did about 272° to 273° of a 360° orbit. So about 3/4ths of an orbit. I am not including the ten minutes it took to get from the launch pad to orbit as being in orbit, nor am I including the 30 minutes it took from the deorbit burn to landing as being in orbit.
Ok, he didn't complete one full orbit. So what? He was in orbit every second of that 3/4ths of an orbit. So, yes, Yuri did indeed go orbital. He didn't need to go 360° to make that claim.
I will posit a definition that you are in orbit, even if only for a portion of an orbit, if your calculated orbital lifetime is at least one orbit. For typical ballistic coefficients, that would be about 150 km. Yuri's orbit was 315 km x 169 km, with a much longer lifetime than one orbit. I calculate about a 19-day lifetime for that orbit and the (relatively high) ballistic coefficient of a Vostok spacecraft pointed into the wind.
It certainly wasn't a sub-orbital flight, as were the flights of Alan Shepard and Gus Grissom which never got close to achieving the speeds required for orbit.