Ṛta, ritual and Buddhism Not "clinging to rites and rituals" is one of the three requirements to become a Sotapanna. 

But in creating a Sangha with strict rules (especially given the extensive permutations within the Tripitaka), the recitation of the Patimokkha etc, do followers of the Dhamma and Vinaya inadvertently accept the usefulness of ritual? Was the Buddha's warning more specifically against any practice that is not grounded in empirical experience?

And given that the Noble Eightfold Path establishes a concrete method and practice for the attainment of the goal, did the Buddha embrace Ṛta - the natural order of the Universe or Truth - if only in its most stripped down, empirical form?
Clinging to rites and rituals

It is mis-belief in something miracle and shortcut. It is mis-belief in worshipping the creator or god can bring the worshipper's liberation/salvation. It is something one is throwing away own efforts and nurturing own knowledge and wisdom. It is just mis-belief in some powerful beings (god) or some powerful things (fire [in some india place people worship to fire]) that ultimate liberation/bliss can be offered/transferred from it. It is mis-belief that the manners, habits and practice of dog or cow(bull) can cleanse one's impurities in mind. 

Noble Eightfold Path

Noble Eightfold Path is one needs to practice oneself. The practitioner of Noble Eightfold Path never expects the salvation from anyone/anything. The very first of the Noble Eightfold Path, Right View already gets rid of the idea of "Clinging to rites and rituals" and so the two path clearly opposite to each other. 

Vinaya

Vinaya is set of rules to monks. The tipitaka indicates that it is purely from Buddha's authoritative order (there is no one who defined Vinaya and only Buddha did). The purpose of Vinaya is clearly stated by Buddha in Vinaya pitaka as follow:


To accept and be disciplined by Sanga that Sanga likes to comply
To be in Sanga with pleasant mind/body by complying Vinaya  
To identify and punish the committed one
Complied monks stay together peacefully/cherishing
To get away from present dangers/prosecutions by broking the law (vinaya)
To get rid of future dangers/sufferings
To be pleased by lay people who has not done to do so
To be more pleased by lay people who already has done to do so
To maintain three Sasana(s) more longer
To promote the vinaya (rules)

So it is the purpose of Vinaya and it is clearly intended to Sanga (the organization of monks) to be followed, disciplined and complied. The lay people is not abided by the Vinaya. 


To attain the Nirvana, it is only one needs to follow the Noble Eightfold Path. It is not necessary to to be part of Sanga, be a monk(eventually it is not necessarily to be disciplined by Vinaya). So Vinaya is optional to lay people and it is only adopted when joining the Sanga. 

For about Rules (Vinaya)

In above 10 purposes of Vinaya, Buddha clearly stated that to get rid of dangers and sufferings by complying it. By following it, one can free from accusing/prosecuting oneself at least. On closer learning of vinaya, it is trying to get rid of Five hindrances to some extent. 

There is another example that would not go deep like above statement. Even in some club membership (and some religious matters) in real world, there are some ridiculous rules need to follow by new members. The only explanation is "it is tradition" and nothing more will be detailed. 

Here is another example also stating that rule is not ritual. For travelers to Singapore it is illegal to bring/consume Chewing Gum but nobody say Singapore is in ritual by applying this law. There are many queer/odd rules applied by a number of countries but it does not totally apply those countries are in ritual. So there is clear distinction between rules and rituals. 

Buddha's vinaya is clearly path-ed/reasoned than those of that. The two reasons (7 and 8) of vinaya on Sanga are because organization of monks (Sanga) is totally relied on offerings (meals, robes, accommodations and medicine) of lay people; in terms of living on donation. So it is very heavy burden for monks to comply rules so that people are pleased to see that their offerings go not in vain (they are not offering things bought by their hard-earned money to total jerks for nothing). 

And another meaningful of vinaya is by following it, the complied person can feel oneself free from harms. Opposite to this, in ritual, the practitioner cannot clearly state why ritual has to be done, the practitioner cannot explain more than it is a tradition, it must be done but no reason. After completing/fulfilling the ritual, there is no obvious proof that result/outcome is achieved. The only thing is forced to believe. Let say a weight-controlling lady avoids any solid food meal after noon and after some days/weeks practicing this she can feel she lost her weight and feel better, healthy and active. Ritual is not close enough this in the sense of "Result oriented".  

In conclusion, Vinaya is not ritual and set of rules bound to Sanga only. It is optional to lay people who follow the Noble Eightfold Path. Vinaya has 10 reasons to be put in place and Vinaya is trying to get rid of bad deeds as much as possible so that the practitioner can please himself and prone to mindfulness (good concentration) but ritual only based on belief (not clearly defined outcome/result of achievement).