Their website doesn't make this clear, but if you look at their Terms & Conditions you can see which airlines they partner with:

"All standard Delta SkyRewards and SkyMiles program rules and conditions apply. Please allow 6-8 weeks for your WorldPerks miles to post to your account. Participation in WorldPerks is subject to the terms and conditions of the WorldPerks Program.
All Midwest Miles Program rules apply.
All OnePass terms and conditions apply.

Southwest Airlines Rapid Rewards Members can receive 0.5 Rapid Rewards credits for each eligible stay or redeem Returns points for Rapid Rewards credits. Guests must be members of Returns to receive Rapid Rewards credits. All Rapid Rewards rules and regulations apply. Eligible rates to receive credits per stay in the Returns program are RACK, PROMO, FTLQ and AAA. Members must select at time of checkin to earn 0.5 credits per stay OR Returns points for that stay."

Ok, so that explains how much Southwest you earn right there. For the rest of the story, I guess you have to visit each of those airline's sites. For example, at aa.com if you go AAdvatnage -> Parners & Milesage Programs -> Hotels, then click La Quinta, you get to a page where it says:

"Members of the Returns Program can now earn 250 AAdvantage miles per stay at any La Quinta hotel. For more information or to become a Returns Program member, visit www.LQ.com online."

Note that this is different the HI Express, in that you earn per stay, rather than per dollar spent. If you want to earn per dollar spent (because you're doing long stays and/or staying in expensive locations), you'll have to earn points and then later convert to miles. (Unfortunately, it looks like you have to sign up for LaQuinta Returns before you can see the conversion rates. But it's free, so you might as well sign up now if you're pretty sure you'll be staying there in the future.)