Sure, the word here is presumably meant to be a portmanteau of "watashi" (私 I, me) plus "ashiato" (足跡 footprint). The ~ato suffix refers to the remains or evidence of something no longer present (e.g. the site where a castle used to be), so the word could also be read as "watashi" (me) + "ato" (evidence left behind).

Either way, basically it's a pun. Not the world's most amazing pun, but it's not gibberish like several commenters have suggested.