Torah Temimah cites Shevuos 7a.
It was taught, Rabbi says: I could read “chayah”; why was “beheimah” said? It is said here “unclean animal” and said there “unclean animal” — just as there it is tumas kodesh, so here it is tumas kodesh.
The gezeirah shavah links the neveilah-contact of this verse to the tumas Mikdash / kodashim framework rather than treating it as a free-standing liability.