Is it true that natural selection is not involved in the mechanism for sympatric speciation?

Natural selection is involved.  The selective pressures are not necessarily the same.  The Galapagos finches are a classic example of adaptive radiation.  If there are two (or more) food sources that are best exploited by individuals with different beak structures (e.g. long and delicate for catching insects, short and heavy to crack tough seeds) the population may diverge where extremes of the population have the advantage.  The selection for extremes is termed disruptive selection.

No the selection pressure comes from intraspecific competition, which is what drives the behavioural changes that eventually lead to the new species. Think of it like two dogs in a yard and they are given one steak and one pumpkin to eat every day. They both want the steak, but only the strongest most dominant one will get it. The other one must eat the vegie or starve. On a community level, if the vegie eaters pass on their DNA and also behaviour to their offspring. Random mutations which arise over time in this sub-population lead to speciation but these may be completely unrelated to the initial requirement to find a different food source, shelter requirement, parenting strategy etc which allowed them to succeed under competitive pressure from conspecifics. This kind of behavioural adaptation is called "niche differentiation."

Long winded (as usual) answer from the fake biologist except that vegetariansm or "vege eating" or in his case mindless fanatic vegansim isn't genetic and therefore cannot be inherited. With two dogs, one will not adapt but die. No new species will emerge but the winning dog will have improved its genetics so that it will be a stronger (but the same) species.

But to follow his argument, the case for human evolution wherein the omnivores or meat eaters have always emerged as the dominant species when they came into contact (and conflict) with the herbivorous hominids.

Sympathetic speciation resulting from spontaneous mutation plays a role but so does natural selection. Geographical pressures vary since geographical features also vary.But several environmental/geographical conditions share commonalities hence the basic similarities of seemingly diverse and unrelated species. Mutations may happen within the same geographical or similar system. But to say that's all  there is is to convenient an excuse. .