I’ve added descriptions for some of the items:
~ = The notation for “immediately afterwards”. It usually means the moves should be inputted very frames apart, but it varies by move and game. eg. Ken’s Kara throw in SFIV is f.mk~lp+lk, pianoing the punches from low to high would be lp~mp~hp
Absolute/Free guard = A game is said to have absolute guard if hits at your level (ie standing or crouching) are blocked automatically while you’re in hitstun. eg. In SFIV, if you block the first hit of Metsu Shoryuken the game will automatically block the rest even if you push forward. Games with free guard require you to manually block regardless of whether you’re not in blockstun.
Hit pause = The slight pause that occurs in some games when moves/projectiles hit the opponent
Juggle = A combo that connects while the opponent is off the ground.
Cancel = To cancel the animation and or properties of one move by using a another.
Chain = A chain is a series of normal moves where the recovery of each move is canceled into the startup of it’s successor, thereby creating a combo.
CPS1 cancels = A type of cancel exclusive to SF2 games which ran on Capcom’s CPS1 hardware (WW, CE, HF) that allowed you to cancel chainable kicks into any punch. The trick was to start with a light chainable kick, and then switch stance from high to low (or vice versa, depending on which move you started the combo with) and press the same kick + any punch. eg. c.lk xx s.lk + s.fp. This was a powerful technique because the punch maintained combo potential so it could be cancelled into a special move (In SF2, CPS1 chains ending in a special usually dizzied the opponent)
Renda cancel aka Renda kara cancel aka Chain Cancel = A technique used primarily in SSF2T to extend a chain combo into special combo (usually Super). In SF2, you could not combo into a special move after a chain combo. You can bypass this limitation though by starting a chain combo with crouching attacks and then kara-cancelling a standing chainable move into a special. eg. To combo into Ken’s Super from two shorts: c.lk xx c.lk [df f d df] xx f.lk~p. SFIV’s Chun Li’s c.lk c.lk into EX legs is also apparently a renda cancel.
Kumite = An organized battle were 1 player squares off against a number of other opponents (usually 5 or more)
Gachi aka Taiman Gachi = A long series of matches (usually 10+) between two players
Feel free to correct any mistakes/oversights
A note on the vortex:
I think the key concept which is missing from the description is that each mixup option resets the vortex if it is landed successfully. Without that aspect it wouldn’t be a vortex, just a plain mixup.