@ Jerry Adams
Good points about current limits. Some rechargeable Li-ion batteries have a built in protection circuit that helps prevent bad things from happening (fire, explosion, venting with flame). These circuits can limit current draw as well as offer low-voltage protection (or over-discharge). This could also be an explanation for your experience of decreased runtime.
Unprotected Li-ion cells used together in parallel or series are very dangerous. Bad things can happen if the cells are unequally charged or one is compromised in some way. Fortunately, most consumer electronics (phones, laptops, power tools, etc) have protection circuits built in to avoid this (as do the batteries linked in the OP).
I don’t have a Steripen, but a simple multimeter could determine the current draw and then it should not be too difficult to find a brand of rechargeables with specs that can match that current draw. But also try to figure out the voltage limitations of the Steripen circuitry before using rechargeables.
@ Roger Caffin
For the AA battery category, Eneloop AAs are a fantastic rechargeable. They have a low self-discharge rate and have a relatively high capacity and high current draw that operates in a pretty wide temperature range. They easily exceed the the performance of alkaline batteries (Duracell, Energizer, etc) in high drain applications. However, you are absolutely correct that Lithium AA primaries are superior in capacity, weight, shelf life, and temperature range over any 1.2V rechargeable.