Well, this is where we get into the nuance of *the developer’s implementation* versus what we fans consider. They clearly made Siam in Civ V Sukhothai empire distinct from Ayutthaya Kingdom. So it’s clear that they have parsed out the nuance between them...
Speaking here as a historian and anthropologist of Thailand and not as someone working for Firaxis, I'll say that I think Ayutthaya has more of a claim to Siam than Sukhothai does. Sukhothai was independent of Siam for a long time and was more in the northern Thai cultural sphere than in the Siamese cultural sphere. As Lanna (Chiang Mai) and Siam (Ayutthaya) competed, eventually Ayutthaya absorbed Sukhothai. And, a long time later, Siam absorbed Lanna as well (although technically speaking those areas are not "Siamese" in the sense of "speaking Siamese Thai").
In the reign of Rama IV, Sukhothai was resurrected to be emblematic of a pre-Khmer "Thai-ness", so that's why it's often considered to be the first Thai state... it's not technically the first Siamese state (that's Ayutthaya), but for people trying to write a national history, it often is used like that.
But what's "Siamese?" It's a good question. These days I use it to refer to states in the Chao Phraya valley from Ayutthaya onward, or to refer to the language we might also call Central Thai. The Internet has simple answers ("it means 'dark!' It means 'golden!' It comes from a Portuguese uptake of a Chinese word!), the truth of which nobody knows. The Khmer identified Siamese subjects in their writing, so we have that, and Chinese sources were calling Siamese "syan". And, further, there seems to be a link between Shan and "Syan" (the Shan are a Tai-speaking people in the north of Burma, related to the people in Chiang Mai). The simple truth is that many people in that region until the colonial era did not think in terms of ethnicity in the same way that European colonizers did.
So... is Ayutthaya Siam? It's a name that was used by outsiders first, and only really taken up later (1700s-1800s) in Siamese history by Siamese themselves. The residents of Ayutthaya would have referred to the city as their identity (i.e.
khon [person]
ayutthaya, and not
khon Siam. Sukhothai residents would certainly not have used the word
siam). Think of words like "Maya," "Indonesia" or "India" here. It's an abstraction, that takes a particular vantage point and looks backwards. In retrospect, can we use the word? I think so, with regards to Ayutthaya. Sukhothai... maybe. But we'd need to ask ourselves why we're using that word, and not
mueang [city, state, polity]
sukhothai instead. Are they both Thai states? Sorta as well - that word, too is new-ish. Certianly they were a key building block to the present-day Thai state. Are they Tai states? Definitely, if we see "Tai" as meaning the larger ethnic category (including Shan, Lanna, Siam, Lao, Zhuang, etc).
I think there would have been better choices for Siam, aside from Ramkhamhaeng (sukritact's mods are on point here), but he'd be on "the list" were I to make such a thing.
TLDR: Ayutthaya is more Siamese than Sukhothai, although Siam
as Siam really gets into its own groove a little later.