What would need to be shown in order to support Lamarkianism is that the methylation patterns are passed on to offspring (and showing that the methylation patterns in childhood were different from those at birth, would probably be helpful as well).
It is fallacious to extrapolate from patterns of reproduction at the cellular level of amino acids to reproduction patterns at the organism level of sperm and egg. It is akin to applying quantum mechanics to billiard balls.
What the study does show is that there are long term effects of childhood living conditions which manifest themselves at the celluar level. Given that we are readily able to observe some effects of childhood living conditions at the macro level of the human organism (e.g. physiological manifestations of diet or altitude), finding their biochemical mode of expression should not be entirely unexpected.