Whether something is or isn't a word is rarely black and white. In dictionaries, the debate is usually played out in the battle between descriptive dictionaries and prescriptive dictionaries.
A dictionary with a descriptive editorial policy is typically sympathetic to describing the changes in language. They're quicker to add new slang, nontraditional words, and informal usages. Think of this approach as one that documents the dynamic shifts in language and usage.
A dictionary with a more prescriptive editorial policy favors correct usage. Its intent is to prescribe how language should be used. Dictionaries that are prescriptive are less likely to acknowledge nontraditional words. They're also more likely to label and editorialize on usage.
Obviously there are many different dictionary publishers, and not one of them can rightly claim to be "the dictionary of record". As a consequence, words can show up in some dictionaries but not in others. Sometimes those words are labeled "nonstandard", "not accepted as standard", "colloquial", etc.
Often whether something is or isn't a word depends simply on your own ideas about language (are you more prescriptive or descriptive?) and what you're doing with it. If you're a copy editor, there's a good chance irregardless isn't a word. I expect you'd cross it out every single time you saw it.
If you're talking informally with friends and family then irregardless might find it's way into the conversation. Most people wouldn't bother with a correction, and I expect all would know what you mean. Given that's what language is supposed to do, then irregardless certainly functions as a word, if not necessarily an agreed upon one.