It's a common misunderstanding to think that the way a dictionary divides headwords is supposed to indicate the syllabification of the word. It doesn't; it's related to the syllabification, but not the same. What it's meant to indicate is where a word can be broken for hyphenation.
You can find more explanation of this in the answer to the following ELU question: Different syllabic boundaries in various dictionaries?
Actual phonetic syllabification is also complicated. Certain words are easy to divide into syllables (e.g. "hangnail" should clearly be divided as /hæŋ.neɪl/) but many others are more difficult. Different scholars have different theories about how to divide words like "barrel", "mattress", "later" and "selfish". John Wells proposed syllabifying these as /bær.əl/, /mætr.əs/, /leɪt.ə/ and /sɛlf.ɪʃ/ respectively.
Your question is not silly.
Both words you've mentioned have two syllables or sounds.
Each syllable in English contains a vowel or a letter that gives a vowel sound. Some syllables are very short and quiet ( we call this sound minor stress because we hardly hear it).
Often we cant sound a syllable clearly because it has a very short/low (unstressed) sound we call schwa'but it is still a vowel.
The word castle can be divided into two syllables = cast + le
Notice each syllable contains a vowel
The word seven also has two syllables = sev+ en
Notice both syllables have a vowel .
Now look at this word: photography.
This word has four syllables and each syllable can be seen if we break it up to see on this page.
Ex pho to gra phy
This has four syllables but the last doesn't have a vowel. However it does contain a vowel sound (from the y).
The word Canada has three syllables = Ca na da.
Each syllable does contain a vowel as seen on paper, but the last sound is hardly pronounced (this is unstressed and doesn't sound like a vowel , so be careful).
One silly way to count out syllables and to find which sounds are major or minor is to pronounce the word as if you are calling your dog back.
Source Teaching American English Pronunciation by Peter Avery/ Susan Ehrlich
Best Answer
The website you linked is unreliable and incorrect. I wouldn't recommend using it (or any other website) syllabification because syllabification is a highly controversial topic in linguistics. How to syllabify a word depends on who pronounces it. For example, the traditional pronunciation of the word film is [fɪlm] (one syllable), but I've certainly heard the disyllabic pronunciation [ˈfɪ.ləm].
The word 'dune' is usually pronounced [djuːn] and 'rider' [ˈɹaɪdə] (BrE). I agree with your analysis that 'dunerider' should be [ˈdjuːn.ɹaɪ.də] (three syllables) (it can also be pronounced in many other ways, though, even four-syllable pronunciation is possible depending on the speaker). It is not pronounced /ˈd(j)uː-n-raɪ-də/ (four syllables), because it suggests that the /n/ is syllabic which it is not. /n/ can only be syllabic when it's preceded by an obstruent (/t s z d/ etc) as in button. I would suggest you use your ears for deciding the number of syllables in a word.
Let's see how 'dunerider' is a three-syllable word:
This is the sonority curve for the word 'dunerider'. The dark blue dots mark the peaks of sonority and the number of peaks correspond to the number of syllables. As you can see, there are three peaks in [ˈdjuːn.ɹaɪ.də], hence three syllables.
The sonority of all phonemes of English can be depicted on a sonority scale (sonority hierarchy). A sonority hierarchy is a hierarchical ranking of speech sounds. Typical order of sonority values is:
Vowels [ɑ, ɔ, ɪ, i] etc > Glides [j, w] > Liquids [ɹ, l] > Nasals [m, n, ŋ] > Fricatives [s, f, θ, ð, z, ʃ] etc > Affricates [d͡ʒ, t͡ʃ]> Plosives [p, b, t, d, k, g]
Vowels are the most sonorous whereas plosives are the least sonorous sounds.
[From my previous answer]
I have explained the Onset Maximisation Principle (syllabification rule) in this answer.