It is worth noting also that though the PLA did not have ranks, that's not to say they didn't have grades and positions, which clearly defined the person's position in the military hierarchy. Even today, the PLA's structure can be a bit confusing to those familiar with Western systems. For example, in the US military, the position of company commander for a line company (eg artillery, infantry, armor) is a Captain's position, an O-3. So that's Billet, Rank and Grade, all the same.* In the PLA, though, grade (jibie) is more synonymous with billet (zhiwu) held than with the rank (junxian). Sure, he's got stars on his shoulders, but look for the ribbon denoting grade, as that's more important. (It's the ribbon on the center of the top row of the salad bar). The salad bar also only shows a combination of grade and years of service, which is why you will see the same ribbons appear repeatedly. The more rows, the higher the grade. Thus, the company commander of a PLA infantry company will wear one row of ribbons, the center ribbon being light blue with two stars. He will also wear on his shoulders the three stars and one line of a captain. If, however, you see another individual wearing three stars and one line of a captain on his shoulders, but his ribbon rack is of two rows, the top center being a dark blue with one star, you know he's a battalion deputy commander. Neither is in a position above or below his rank.
Thus, in the period 1965-1988, one would not look for rank insignia and address the Comrade Major, one would look at the grade insignia and address the Comrade Battalion Commander. The grades were meshed with the National Administrative Cadre system which had 27 grades for officers. This was reduced to 23 in 1972, and the current 15 grades in 1979. Each grade is grouped into, for lack of a better term, one of seven grade groups. Thus, the Chinese Chief of the Military Staff will have seven ribbon rows, which added together will reveal years of service, and the top center ribbon being a yellow one with a wreathed star. The ten ranks are assigned across the fifteen grades, the grades generally equalling billets.
You get the idea, I hope.
So, there very definitely was a rank structure in the Chinese military between 1965 and 1988, they just didn't call it ranks, since 'rank' has a somewhat different connotation in the Chinese military.
Of course, battle uniforms would not have had the salad bar, so determining rank... sorry... billet in the field could well have been a bit confusing if you didn't happen to know the chap on sight.
In the end, of course, the Chinese decided that there was probably a reason why every other military in the world was keeping ranks, and went back to it. They recently announced, however, a conversion in the system which basically equates rank with billet, in conjunction with the rest of the world, since the convoluted and unique system the Chinese use was a bit confusing to members of other forces the PLA was interacting with. There is precedent: A sergeant (two stripes) in the Irish Army in the 1960s would out-rank a three-stripe-and-a-rocker US staff sergeant, but try convincing the American of that. As a result, given Ireland's move to be heavily involved in international operations, the ranks were changed so there is no one-stripe, corporals have two, and sergeants three.
*To be sure, it is possible to find a lieutenant in that position, so the rank would not match the billet, but such situations are usually understood to be temporary pending either the paperwork for promotion catching up, or replacement with another captain.