I would recommend having your lawyer review the terms to ensure you’re in compliance. We can’t comment in-depth about legal concerns, which is likely why there were no responses from integrationsuccess. I would point you to two particular sections and clauses of interest, aside from the one above, in the Developer Agreement:
Section:
III. Ownership and Feedback
A. Ownership of Program Materials.
Schedule 1: Storage of Program Materials/Twitch Content
Do not store copies of Twitch Content and Program Materials, unless you (a) obtain authorization (through these terms or otherwise); (b) control the rights associated with such content; or (c) cache such information for only a twenty-four hour time period without further sharing it with third parties.