That's what "technical analysis" means in the finance world, though... so, am I missing a joke?

Technical analysis is the projection of future price data through analysis of past price data (usually for the purpose of trying to create trendlines or find "patterns"). Options pricing is quite a different beast - it encodes marketwide uncertainty about the future price of the underlying, which has little to do with the past price action of the underlying, and everything to do with all known information about the actual underlying company, including fundamentals analysis, market sentiment, future expectations and risks, etc.

To put it another way, to price an option I need a) the current price of the underlying, b) the time until option expiry, c) the strike price of the option, and d) the collective expectation of how much the underlying's price will vary over the period between now and expiry. This last piece is "volatility", and is the only piece that can't be empirically measured; instead, through price discovery on a sufficiently liquid contract, we can reparameterize the formula to empirically derive the volatility expectation which satisfies that current price (or "implied volatility"). Due to the efficient market hypothesis, we can generally treat this as a best-effort proxy for all public information about the underlying. None of this calculation requires any measurement or analysis of the underlying's past price action, patterns, etc. The options price will necessarily include TA traders' sentiments about the underlying based on their TA (or whatever else), just as it will include fundamentals traders' sentiments (and, if you're quick and savvy enough, insiders' advance knowledge!) The price fundamentally reflects market sentiment about the future, not some projection of trends from the past.