"not by a long shot," presumably a reference to some type of competition, such as a horse race, where a probable loser is called a long shot

From a Britlish perspective, slithy:
In a horse race, I'd call horses less likely to win "outsiders", not long shots. If you placed a bet on one of these you would be "taking a long shot". In other words, the long shot is your bet rather than the horse.

The most common use of "long chalk" I've heard is:
"Did your horse/team/whatever win?"
"Not by a long chalk"
Interesting that I've only ever heard "long chalk" statements in the past tense, never as predictions.
"He'll win by a long chalk" and "He won't win by a long chalk" sound very strange.

At least here in the South of England, dominoes aren't played like they used to be, which is a shame. However, as far as I'm aware, pen and paper has taken the place of chalk marks.

I reckon a "long chalk" may be the long diagonal line you draw over the preceding 4 vertical marks on every 5th point (as per marking off the days in a prison cell - counting without numbers). In other words, winning by a long chalk is winning by 5 points, which makes for a clear win when the marks are side by side. Total supposition, but feels plausible.