It's a tortured article and I think the author may also have English as a second language
...it could benefit from a good proofreader's pen.
Anyway the gist of the whole thing is really the conclusion:
In conclusion, a low plasma level of antioxidant vitamin E was demonstrated in patients with active variant angina but not in patients with the inactive stage of variant angina, suggesting that the plasma status of vitamin E is linked to the activity of coronary artery spasm.
The LDL discussion is just ancillary (extra) and points to the POSSIBILITY that the shortage of Vitamin E might cause more oxidation of LDL and that the oxidized LDL might be a vasoconstictor, causing spasm.
They sought to examine the relationship (not necessarily cause and effect) of Vitamin E and variant angina and found some reasonable correlation. Little more should be drawn than that!
I hope that helped a bit.