First -- do go back repeatedly over several weeks and see if this is the daily norm for this cafeteria or if perhaps you caught it on a day when (a) the kids were wound up from something (an assembly? A fire drill? Bring your toy to school day?) or (b) the parents supervising were just particularly wimpy about stopping these shenanigans (maybe other days, other parent volunteers keep better order). Check it out more than once before taking action. But DO take actioin if this is the norm.
I would bet the lack of supervision is at least partly because the "supervisors" are, other than the principal, parent volunteers. Many parents will willingly tell someone else's kid to stop doing something, or will remove them from one place to another, or take away something out of that child's hands -- but many other parents are not willing to do those things because they fear beiing seen as "parenting someone else's child" or fear the kids will whine to mom and dad about how someone else's mom dared tell them to sit down or quiet down.
How are the volunteers organized? Is there a regular, formal roster of who has cafeteria duty and when, or is it all too casual? Are they trained in ANY way, even a talk by a more experienced parent who has done it? Or are they parents who just turn up -- maybe because their own kids are having issues with all the chaos in this lunchroom, so the volunteers really are there to make sure their own kids are not going hungry and getting stressed? (I would not blame them for that!)
If you continue to see a chaotic cafeteria, I would put in writing what you saw, exact date and time included and exact incidents too. Give it to the principal and ask for a meeting. Before that you might consider getting other concerned parents involved so it's not just "Oh, that one mom is so uptight about lunch...." I'm sure other parents might be willing to come with you to meet the principal.
This level of chaos, if it's daily, is very bad for learning, not just lunching. My friend's son has had serious issues in their lunchroom (second grade) and it has spilled over into the classroom -- the kids who are wildest in the lunchroom are wildest in the classroom, and after a wound-up lunch everyone returns to the classroom wound up and wild.
If the principal won't get involved or says (my friend's son's school said this) "We don't have money for paid supervisors for the lunchroom," get the PTA involved, see if you can organize a formal roster, and be CLEAR what the volunteer parents are there to do and how far they can go: Can they tell a child to sit down? To take hands off another child? To move to another seat in order to separate two kids who are too wild when together? It's sad to have to be that specific but you may have to be.
If your school needs more lunch tables find out if the PTA can find or raise funds for them, perhaps. But be sure first that the school will permit them -- you might hear "We don't have room" or "More tables would put us in violation of the fire code because we can only have X tables in that space." You may be amazed at the obstacles you could have tossed at you in an attempt to calm down this cafeteria. But if parents don't get involved now and show the administration they really mean business, by the time these kids are in higher grades it could be worse, as it has been at my friend's school.