My reservations about the clarity of the question weigh sufficiently that I should first list and explain those reservations before answering the question as I understand it.
- 'Right' does not mean 'clockwise'. That the words sometimes mean, in absolute and relative terms respectively, the same direction, is happenstance at most, accidence or coincidence at least. No etymological or necessary semantic connection between the terms exists, so far as I can determine.
- Similarly, while some may say "right and left in lieu of clockwise and counterclockwise" (Original Post, OP), I am not one of them. I am much more likely to go the other way around (say 'clockwise' in explaining 'right' etc.), but if pressed by somebody who does not know which is which, will usually immediately retreat to gestures (pointing), a known relative direction ("toward downtown" for example), or another absolute direction ("toward the setting sun"), rather than using 'right' or 'left' to define 'clockwise' or 'counterclockwise' or the other way around.
Wikipedia notwithstanding, 'deasil' (var.) is not usually thought to "derive from" Latin dexter. Rather, Gaelic deas and Latin dexter are cognate, where 'cognate' means
Of words: Coming naturally from the same root, or representing the same original word, with differences due to subsequent separate phonetic development....
OED, cognate, adj., sense A2a.
Perhaps a side note is that Wikipedia's entry for "Clockwise" is...chronologically imprecise (to put it politely). Logically speaking, the claim in the entry that before "clocks were commonplace, the terms 'sunwise' and 'deasil'...were used for clockwise" suffers from omitting to mention the period before clocks existed, that is, the period when no word was used for 'clockwise'.
An explanation of "the association between linear and circular directions" (OP) does not seem pertinent to the question. Supposing the question conflates the exact geometrical definition of 'circle',
In Geom. defined as a plane figure bounded by a single curved line, called the circumference, which is everywhere equally distant from a point within, called the centre. But often applied to the circumference alone, without the included space.
OED, circle, n., sense I1a, emphasis mine.
with the frequent application of that definition to the circumference alone, then the 'linear' direction is not distinct from the 'circular' direction; both are lines, whether or not one is curved. If, on the other hand, the conflation of the technical definition of 'circle' and the usual application of that definition to the curved line alone was not intended, but rather the distinction between a line and a plane, it is not clear to me how, or if, that distinction involves 'to the right' and 'clockwise'.
- Supposing that the question intends to ask "why is clockwise to the right?", it is not an English language question, but rather a historical question that can be answered (albeit simplistically) with (a) the observation that 'clockwise' is not always or necessarily 'to the right', as evidenced by clocks with the opposite motion, along with (b) a historical sketch of the development of clocks in the Northern Hemisphere from sundials themselves developed in accordance with prevalent religious beliefs and practices.
Having noted those reservations, my understanding of the question becomes something like this:
How is it that 'to the right' on the horizontal plane came to be projected onto the vertical plane?
To my surprise, a semi-linguistic answer based on etymology can be offered.
That answer lies in the dual meaning of the Gaelic root of 'deasil', deas: deas means both 'right-hand' and 'south':
... < deas right hand, south, in Old Irish dess, des, Welsh dehau, cognate with Latin dexter, Greek δεξιός. (The meaning of the latter part is unknown.)
OED, extract from the etymology given for deasil | deiseal, adv. and n.
OED's first attestation of 'deasil' (in the form 'deasoil') is a quote from the first edition (1771) of Thomas Pennant's A Tour in Scotland MDCCLXIX (MDCCLXIX = 1769). Here is the quote from Pennant in context (fourth edition, 1776):
Druidism having been the form of religion in this country [Scotland] before Christianity, the people still retain some superstitious customs of that Pagan religion...at marriages and baptisms they make a procession around the church, Deasoil, i.e. sunways, because the sun was the immediate object of the Druids' worship.
This might seem to beg the question: why was the procession to the right on the horizontal plane considered "sunways", when the sun's apparent movement is on a vertical plane?
The answer is that 'sunways' describes the direction an observer in the Northern Hemisphere turns when observing the sun's passage across the sky; observers of that movement, whether standing, sitting or lying down, must turn at least their eyes to the south (deas) and to the right (also deas). Thus the horizontal plane of the observer's motion translates to the vertical plane of the sun's movement.
Part 2 of Pennant's A Tour in Scotland MDCCLXXII (MDCCLXXII = 1772) sheds a little more light on the issue. What OED describes as "unknown", that is, the meaning of the '-sil' or '-il' portion of 'deasil' (see OED etymology shown above), Pennant confidently translates as deriving from "Syl, the sun". See the daggered note in this clipping:
If Pennant's derivation is correct (which, notably, OED does not confirm), the horizontal plane implied by 'to the right' is joined with the vertical plane of the sun's movement in the two parts of the word describing both, 'deasil':
Righthandwise, towards the right; motion with continuous turning to the right, as in going round an object with the right hand towards it, or in the same direction as the hands of a clock, or the apparent course of the sun (a practice held auspicious by the Celts).
OED, deasil | deiseal, adv. and n., emphasis mine.
An earlier attestation than the first, 1771 quotation provided by OED agrees in substance with Pennant's derivation of the second part of 'deasil' ('-sil'), and confirms the specifics of the belief system described by Pennant. The 1726 publication A Collection of Several Pieces of Mr. John Toland provides this narrative (bold emphasis mine), where 'deasil' appears in the form 'deiseal':
The vulgar in the Ilands do still show a great respect for the Druid's houses, and never come to the antient sacrificeing and fire-hallowing Carns, but they walk three times round them from east to west, according to the course of the Sun. This sanctify'd tour or round by the south, is call'd (91) Deiseal as the unhallow'd contrary one by the north (92) Tuapholl. But the Irish and Albanian Scots do not derive the first (as a certain friend of mine imagin'd) from Di-sul, which signifies Sunday in Armorican British, as Dydh-Syl in Welsh and De-zil in Cornish do the same; but from (93) Deas, the right (understanding hand) and Soil, one of the antient names of the Sun, the right hand in this round being ever next the heap. The Protestants in the Hebrides are almost as much addicted to the Deisiol, as the Papists. Hereby it may be seen, how hard it is to eradicate inveterate Superstition. This custom was us'd three thousand years ago, and God knows how long before, by their ancestors the antient Gauls of the same religion with them; who turn'd round right-hand-wise, when they worship'd their Gods, as (94) Atheneus informs us out of Posidonius a much elder writer.
(93) Item Deis.
(94) [Illegible in reproduction of MS.]