How do I make my roti dough stretch thinner?
I would guess your main problem is the protein in the flour.  To get that stretchy dough that will not tear you need bread flour.  Your water, the proportion between kneading and resting of the dough, and the salt also matter.  The recipe you are using has way too much fat in the dough.  The leaner version suggested by bonCodigo is closer to the needed proportions.

YouTube has a video channel on roti canai.

Flour.  You can buy roti flour from an ethnic grocery store, but many of the chain supermarkets in the US now carry bread flour.  It has higher protein content without being whole grain.  Different flours have different proportions of gluten.  Those with lower content (called weak flours) being better for cakes and those higher content (strong flours), better for breads.  Gluten is not one protein, but a mixture of two protein families: gliadins, which give the dough its plasticity, and glutenins, which give the dough its strength.  Different strains of wheat have different ratios of gliadins to glutenins, hence the need to find an appropriate flour.  In the US and Canada, high protein flours tend to be optimized for loaf breads and not flat breads, so some hunting around for a good brand may be needed.

Ghee  The recipes on the net vary dramatically in the amount of fat added to the dough.  The basic process of dough making is to get the water to break up the gluten in the flour and then stretch those giant molecules to create a network of stringy, tangled molecules.  Too much fat interferes with this process.  About 5g of fat for every 100g of flour is a good ratio.  As ghee adds flavor, the trick to make a dough with higher ghee content is to think of it as a croissant and fold the fat in after the dough has incorporated some water.  This is done by brushing the ghee in later stages of stretch and fold.

Kneading and resting  Making the network of gluten proteins requires energetic changes. Lots of water and rest could do it (as in no-knead breads) and so could a little water, a little rest, and a lot of kneading.  With flat breads one does not need to wait for the yeasts to create the bubbles in the dough. The resting is for the water to do its work of untangling the gluten.  The trick is to know if the water activity, resting, and kneading have brought the dough to the right point.  There are many dough tests that are better explained through a video.  The dough in the leaner recipe is a wetter dough that is a bit trickier to knead by hand.  The basic idea is to place it on an oiled countertop, pinch a corner, and fold it over.  Repeat a few times and it will become easier to handle without having to add extra flour as it often suggested.

Water.  Don't use tap water.  It may be too alkaline, to hard, or too chlorinated.  Andrew Whitley in his Bread Matters book has a chapter on how guilty he felt using Evian to make his bread, but it improved his bread.  For flat breads one is less worried that the chlorine in the water will kill the yeast, but depending on your tap water composition, the other chemicals could be an issue.