It means that if you use the software, you _either_ accepted the EULA _or_ you committed an act of copyright infringement.
It would be interesting to see what specialist lawyers in various jurisdictions would make of that argument.
If when you use the software you also rely on any permission granted by the EULA that you wouldn't otherwise have, this could be instant game-over if it was considered to imply that you had agreed to the EULA as a contract for that reason instead. And if you explicit agreed to the EULA to download the software in the first place, that's probably instant game-over as well. But if you were relying on the EULA only as a licence, not as a contract, and you were not doing anything that requires more than that licence, it does seem like claiming that you infringed copyright instead might be a reasonable position.
However, a more promising alternative, rather than accepting that you've done anything wrong or consented to anything dubious at all just because some dubious EULA term claimed you did, might be to consider recent changes to the legal position in some jurisdictions. Particularly in Europe, many of the usual complaints about EULAs have been considered more thoroughly in recent years, and in some cases laws have been or are being changed to clarify consumer rights in terms of software, downloaded content, and related areas.
That debate typically starts with the perennial question of whether an EULA necessarily creates any binding contract at all, and if it does, whether the terms of such a contract are fair. It looks like the direction we're heading, at least in Europe and more specifically the UK, is that EULA-as-contract can be valid as a general principle, but then those agreements are also subject to the full weight of consumer protection laws just like any other consumer contract. That means a general requirement for fairness in the terms, various more specific protections like prohibiting certain exclusions entirely, and hopefully also the power for regulators to step in preemptively where unfair terms are present, even if those terms are void anyway, so no more incorporating scary-sounding but unenforceable terms to try to divert consumers from exercising their legal rights.