It's a determiner.
'would' is a verb and 'all' is an adjective.
All subjects are part of speech for they are all nouns.
"Say" is a verb.
"That'll" is not a part of speech at all; it is a contraction for "that will", in which "that" is a pronoun and "will" an auxiliary verb.
NOUN
I say it's a verb
A verb.
Adjective.
adverb
All word in the English language have at least one part of speech. Contraptions is a noun, the plural form of contraption.
In this sentence all is a determiner.
Adjective