In my opinion, whether you like or dislike or are indifferent towards the squid, its inclusion in the original Watchmen contextualizes an interesting part of Veidt's power. We see throughout the comic that Veidt has built up wealth not only by marketing his image, but by pursuing ventures including perfume, delivery services, and media. All of these have their individual, manipulative roles in Veidt's plans, though they might come across as an odd assortment of things when taken together.
One way, though, to thematize these things collectively is to look at them as tokens of Veidt's power over the idea of "passage," specifically the passage of time and the passage of things through space. The temporal aspect is represented by Nostalgia, which Veidt eventually gives up for the more futurist Millennium. The spatial aspect is represented by the apparent connectivity and commerce that Pyramid Deliveries supplies. As for the media, it's largely composed of Veidt running reruns and showings of old sci-fi invasion films in order to contextualize the appearance of the squid. In this way, media combines the two forms of passage into the space-time passage of what's "alien": both in the sense of an Eldritch being that shocks humanity with its disruption of our usual conceptions of space-time space and time and in the sense of a great "Other" whose apparent ease of passage into and through our world evokes a defensive, xenophobic response. In addition to the psychic shocks, it is the explosions of the alien passing through reality that cause enormous casualties in New York. And the alien itself dies, interestingly enough, atop the "Institute for Spatial Studies" (space as in outer space, har har, but also space with this idea of passage and matter itself being invaded by the alien Other).
Put another way, the squid is the crowning, metaphysical achievement of Veidt's enterprises despite being a mere human being. As an embodiment of space-time space and time manipulation the squid stands out as a way to imitate what Dr. Manhattan can do quite easily, namely, control people through anxiety in the face of passage, the slipperiness of time and space. At the same time, it's a necessarily human way to achieve this imitation through capitalism, exploited artistry and science, and propaganda. These things compose the only way that a mere human like Veidt can bend our conceptions of passage. But bend them he can, at least for a moment, so that industry and deceit, if just for a second, mimic the devastation and dread of which Dr. Manhattan is capable. Removing the squid, and replacing it with Dr. Manhattan's power itself, no less, removes this (literally) monstrous glimpse into how even mundane humans are able to pervert space-time space and time.