Here's how it works:
1. The Red-Headed League: A fake organization, seemingly unrelated to anything important.
2. The "Universal" Connection: Clay's accomplice, Vincent Spaulding (actually an alias), is a red-headed man hired to join the league. This makes it seem like the league's activities are important to the "Universal" company, which is where Spaulding works.
3. Misdirection: This connection is designed to make Holmes focus his investigation on the Universal company, while the real target is the bank underneath the office.
4. The Real Struggle: The real struggle is between Holmes and Clay's criminal plan. Clay uses the Red-Headed League to divert the attention of the bank's staff and allow him to tunnel into the vault.
Essentially, the "Universal struggle" is a false trail designed to throw Holmes off the scent. It represents the villain's attempt to mislead Holmes, rather than a direct conflict.