It is lawful under the EA2010 for events to be organised for groups who share a protected characteristic - sex, in this case.
I'm still no expert on the law, but I don't think that's true in general - it would likely be discrimination on the basis of a protected characteristic - although there are exceptions, including for physical sport, for women-only shortlists, and for cases where positive action is justified. Section 150 of the EA2010:
If a person (P) reasonably thinks that [...] participation in an activity by persons who share a protected characteristic is disproportionately low [then] this Act does not prohibit P from taking any action which is a proportionate means of achieving the aim of [...] enabling or encouraging persons who share the protected characteristic to participate in that activity.
I think that means that a women-only chess tournament would be legal, but a men-only one would not be.