「烎」, in this slang usage context, came from the name of an e-sports team named 「烎之隊」 ("Team 烎"). The team name went viral after one of their matches against the champions at that time in a DOTA competition, where they were a relatively lower-ranked team but put on an incredibly aggressive match against the champion-title-holding opponent (who was much higher-ranked). The match later became a classic among DOTA fans and the slang meaning came from the aggressive, passionately competitive style that they showed during the match, matching a much tougher opponent by raising their own level.
I believe that 「烎」 is always pronounced yín in this context (and not kāihuǒ). This is because yín is known to hold the slang meanings above, while kāihuǒ does not. I also can't find anything about a contraction of 2 syllables like kuǒ, so I think such a contraction doesn't exist.
As for its original usage, dictionaries say that 「烎」 was originally a word from some kind of topolect, with fǎnqiè 「夷針切」(pronounced as 「淫」, MC: yim, Mandarin: yín), and has the meaning bright1. Its actual use in literature is incredibly rare, and from a quick glance, I can't actually tell if any supposed use is real or from a copying / digitalisation / transcription error. Comments on 「烎」 being a variant of 「㶣」 should be interpreted very carefully2 (and are also actually irrelevant for this slang usage, because the slang usage isn't written with anything other than 「烎」).
Its composition, 「⿱幵火」, is also opaque; while 「火」 is likely semantic (compare 「燦爛」,「煌」, etc.), 「幵」 (MC: ken, even, level)3 is not obviously a hint for yim or bright. Given that this character is rare and was originally from a topolect usage, I don't believe its composition is easily determinable.
The e-sports team reviving this ancient character for use in a name is the same kind of online trend as reviving 「囧」 because it looks kind of like a face. Ostensibly, 「烎」 was chosen to grab people's attention (due to its rarity) and because it looks like kāihuǒ (Open fire! > Attack!) to Simplified Chinese users.
Footnotes:
《集韻・卷四・二十一侵》
「淫」：夷針切。。。。。。「㶣」、「烎」：方言。明也。
When you see the statement "X is a variant of Y", make sure you read it as "X is a variant of Y when used in the context Z", where "Z" is a concrete word with a meaning and pronunciation. If you can't determine what "Z" is, or can't verify any of "X", "Y", or "Z" using some quote from an excavated or received text, then "X is a variant of Y" doesn't actually have any meaning. Looking up another old dictionary does not count as verification, because most old dictionaries are part of an echo chamber quoting even older dictionaries.
「幵」 (MC: ken) is sometimes seen as a component in characters we use today; for example, it is the sound component in 「研」 (ngenH).
References:
