I agree that "I would rather" is better, but I don't agree that "I had rather" is archaic, I think it's a more recent bastardization of the contraction "I'd rather." The reason I think so is that "would" is an ancient and valid conditional form of will, as in want, and that it was thus the original, correct form, which survives in our more conservative North American English. British English has lots of similar corruptions of our more ancient forms. I had rather doesn't really make sense except as a past tense. Another example: we still distinguish between the adjective round and the adverb around, whereas BE has them both chopped off to "round".
Whether it is correct or not, 'I had rather play than work' is clearly an ancient structure. The Oxford English Dictionary gives this example from 1340: 'We had leyuer euermare to serue in egipte..yen in ye wildernes to dey.' (We had liefer (= rather) serve in Egypt for ever more than die in the wilderness).
I see 'had' as an example of the 'past' subjunctive, meaning 'would have accepted'. The sentence can be paraphrased, I suppose as 'I would have accepted the state of the world more easily if I had been playing and not working' (meaning 22a of the verb have in the OED).
By the way, the difference between 'past' and 'present' subjunctives in this context is not really a matter of time: rather the 'present' subjunctive is used of things that may be true; whereas the 'past' subjunctive is used of things that are not true.