I think it likely has as much to do with the sun finally shining for the first time and the daytime temp getting above 50 degrees for the first time since last October. All those Ohioans wanted to take in a warm, sunny day.
I have not been to an OSU Spring Game. I have attended a UF spring game, as my oldest daughter graduated from UF last year. From what I gather, OSU makes their Spring game a fan experience. Troy Smith returned and had a football passing competition with Cardele Jones and JT Barrett. Surplus athletic gear (football, basketball, swimming, wrestling, etc.) was on sale for fans to buy. A 5K ends at the 50 yard line of Ohio Stadium. ETc. OSU has had over 90,000 for most of their Spring games in the 2000s. The national championship definitely helps, but its the fan experience thing that brings them in. The UF Spring game that I saw was boring. Just a practice with a few plays thrown in. We stayed for 30 minutes and left.