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.
I don't think anybody's called it out and out gibberish, just awkward and unnatural because The reading watashi for 私 is rarely if ever used in compounds.
If I was asked to invent the word I'd read the same characters as shiseki (私跡), or go with something like 自跡 jiseki "self-tracks". Although even that sounds more like "ruin of self" than what the author is trying to convey.
Hmm, I don't agree at all on the reading - for an ad-hoc coinage, ～跡 is realistically always going to be ~ato. Like if you jokingly referred to a paw print as 犬跡, saying inuato would be clear to any listener, and saying kenseki definitely wouldn't.
But more to the point, the person I originally replied suggested that the coinage in TFA just used Japanese to sound exotic, so that's what I was replying to. It may or not be great wordplay, but it's certainly Japanese wordplay.
